Get live statistics and analysis of Shubhu 's profile on X / Twitter Archetype analysis The Innovator Shubhu is a tech enthusiast and hands-on creator always pushing the boundaries of software development and emerging technologies. With a deep passion for math, machine learning, and blockchain, Shubhu crafts insightful, educational content aimed at demystifying complex concepts. Their tweets blend technical prowess with approachable explanations, making them a go-to for both peers and newcomers.
🔥 Roast Shubhu tweets so many deep tech threads they could probably give a TED talk on why normal people don't tweet back—maybe it’s not that they don’t care, just that their brains short-circuit at 'differential calculus engine in C++'.
⚡️ Nice achievement Successfully launched and presented a comprehensive differential calculus engine that visualizes step-by-step calculations, marking a standout achievement in combining education with hands-on software innovation.
🌟 Life's purpose To innovate and educate by building practical tools and sharing cutting-edge knowledge that empowers others to understand and engage with advanced technological concepts like calculus engines, machine learning, and Web3.
💬 Values and Beliefs Shubhu believes in democratizing technology and knowledge, embracing decentralization and transparency, and the power of community-driven innovation. They value clarity in communication and are committed to making complex ideas accessible and relatable.
💪 Strength Exceptional technical skills combined with the ability to break down complicated subjects into digestible, engaging content; a natural educator and innovator who creates original tools and thoughtful commentary on advanced tech topics.
🫣 Weakness While deeply knowledgeable, Shubhu’s communication might sometimes be overwhelmed by technical depth or niche focus, potentially limiting broader audience engagement. Also, with a following undefined and high following count, they might not yet have full control over their network growth and influence.
⚡️ Growth audience tips Focus on consistently weaving storytelling and relatable analogies into tweets to build a wider audience. Engaging more with followers through Q&A threads and behind-the-scenes looks at coding projects could amplify reach. Using hashtags strategically and spotlighting simpler beginner-friendly content alongside deep dives will diversify and grow their audience on X.
💁 Bonus Fun fact: Shubhu developed a mathematics engine (v0) for differential calculus in C++ that not only calculates derivatives but also visualizes step-by-step differentiation with 2D graph comparisons, showing a knack for translating theory into interactive tech.
Top tweets of ShubhuThis boy literally really tried in a very good way to understand and explain web3, but for the folks, who literally don't know anything about this -- let me explain this for you and will try to be in more non-technical way.
Web2 is like playing cricket in Ambani’s stadium shiny, big, but he owns the ground, the bat, even the scoreboard. You can play, but the rules are his. Web3 is gali cricket everyone brings their own bat and ball, rules are agreed by the players, and no dadaji controls the match.
Now, the engine behind Web3 is blockchain. Think of it as the class attendance register. Every transaction is a line in ink, every kid keeps a photocopy. Try to erase your bunk day? Forty kids will scream “cheating!” That’s why it’s tamper‑proof.
But don’t confuse the two: Blockchain ≠ Web3.
Blockchain is just the register. Web3 is all the games, apps, and tokens people build using that register. One is the road, the other is the traffic, shops, and dhabas on it.
Decentralisation?
Simple. Instead of one teacher marking attendance, the whole class checks. More eyes = harder to cheat. Slower sometimes, but fairer.
Now, chains. Each chain is like a different school. Ethereum (EVM) is the big govt school, common language, lots of students, sometimes crowded.
Solana is the fancy private school super fast scanners at the gate, but not everyone speaks the same syllabus.
Coins are the school currency (fees, snacks).
Tokens are coupons (game points, votes).
NFTs are unique trophies like that one rare cricket sticker you can prove is yours because the register says so.
And when the main school gets too crowded, you get Layer 2s after‑school clubs that run games faster and cheaper, then report results back to the main register. Base is one such club.
So in short: Web2 gave us playgrounds owned by companies. Web3 is us building our own playgrounds, with our own rules. Sometimes messy, sometimes fun but at least the bat is finally in your hands.”
Most engaged tweets of ShubhuPeople with Innovator archetype Explore Related Archetypes If you enjoy the innovator profiles, you might also like these personality types:
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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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more money on flight tickets @ilavanyajain https://t.co/1xVQM0xFFV","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":0,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[14,62],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[{"id_str":"1561237983751438336","name":"lav","screen_name":"ilavanyajain","indices":[0,13]}]},"favorited":false,"in_reply_to_screen_name":"ilavanyajain","lang":"en","retweeted":false,"fact_check":null,"id":"1979205992509309228","view_count":38,"bookmark_count":0,"created_at":1760714455000,"favorite_count":0,"quote_count":0,"reply_count":1,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1979205565722067188","full_text":"@ilavanyajain what's scary than missing the flight, le mummy -","in_reply_to_user_id_str":"1561237983751438336","in_reply_to_status_id_str":"1979205565722067188","is_quote_status":0,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[10,41],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[{"id_str":"1808455867395661824","name":"Humi","screen_name":"byteHumi","indices":[0,9]}]},"favorited":false,"in_reply_to_screen_name":"byteHumi","lang":"en","retweeted":false,"fact_check":null,"id":"1979238468002738520","view_count":5,"bookmark_count":0,"created_at":1760722197000,"favorite_count":0,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1979232022943129859","full_text":"@byteHumi happy birthday!\nparty kidhr hai","in_reply_to_user_id_str":"1808455867395661824","in_reply_to_status_id_str":"1979232022943129859","is_quote_status":0,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[21,58],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[{"id_str":"1508022250649550864","name":"Superteam India","screen_name":"SuperteamIN","indices":[0,12]},{"id_str":"951329744804392960","name":"Solana","screen_name":"solana","indices":[13,20]},{"id_str":"913141185966833665","name":"Chirag Jani","screen_name":"chiragjani001","indices":[44,58]}]},"favorited":false,"in_reply_to_screen_name":"SuperteamIN","lang":"et","retweeted":false,"fact_check":null,"id":"1979232768916705434","view_count":97,"bookmark_count":0,"created_at":1760720839000,"favorite_count":1,"quote_count":0,"reply_count":1,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1979200649515426232","full_text":"@SuperteamIN @solana let's go, kya kehte ho @chiragjani001","in_reply_to_user_id_str":"1508022250649550864","in_reply_to_status_id_str":"1979200649515426232","is_quote_status":0,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[14,34],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[{"id_str":"1561237983751438336","name":"lav","screen_name":"ilavanyajain","indices":[0,13]}]},"favorited":false,"in_reply_to_screen_name":"ilavanyajain","lang":"en","retweeted":false,"fact_check":null,"id":"1979248681338491287","view_count":161,"bookmark_count":0,"created_at":1760724632000,"favorite_count":0,"quote_count":0,"reply_count":2,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1979248351809015827","full_text":"@ilavanyajain are you able to run?","in_reply_to_user_id_str":"1561237983751438336","in_reply_to_status_id_str":"1979248351809015827","is_quote_status":0,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[13,37],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[{"id_str":"1692679801163993088","name":"major tom","screen_name":"tailwiinder","indices":[0,12]}]},"favorited":false,"in_reply_to_screen_name":"tailwiinder","lang":"en","retweeted":false,"fact_check":null,"id":"1979259551644836327","view_count":105,"bookmark_count":0,"created_at":1760727224000,"favorite_count":0,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1979248926013485210","full_text":"@tailwiinder what's special about it?","in_reply_to_user_id_str":"1692679801163993088","in_reply_to_status_id_str":"1979248926013485210","is_quote_status":0,"is_ai":null,"ai_score":null}]},{"label":"2025-10-19","value":1,"startTime":1760745600000,"endTime":1760832000000,"tweets":[{"bookmarked":false,"display_text_range":[0,44],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[{"id_str":"1342961741718810632","name":"Monad (mainnet 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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Basics of Kerr Metric\nA Kerr black hole represents a rotating black hole. The spacetime geometry (metric) in\nBoyer-Lindquist coordinates is:\nds² = -(1 - 2Mr/Σ)dt² - (4Mar sin²θ/Σ)dtdφ + (Σ/∆)dr² + Σdθ² + [(r² + a²)² - a²∆ sin²θ]sin²θ/Σ dφ²\nWhere: Σ = r² + a²cos²θ, ∆ = r² - 2Mr + a², and a is the spin of the black hole (J/M).\nFor a = 0 → Schwarzschild (non-rotating); for a = M → extremal Kerr.\n2. Event Horizons\nHorizons occur where \n∆ = 0: r± = M ± √(M² - a²).\nOuter horizon (r■) – event horizon; Inner horizon (r■) – Cauchy horizon.\nExamples: \na=0 → r■=2M; a=0.9M → r■≈1.44M; a=0.998M → r■≈1.06M.\n3. Ergosphere\nRegion where r < M + √(M² - a²cos²θ). Inside it, nothing can stay still everything is dragged by rotation.\n4. Photon Sphere & ISCO\nPhoton sphere: where light can orbit the hole (r=3M for Schwarzschild). ISCO (Innermost Stable Circular Orbit) moves inward as spin increases.\n5. Photon Trajectories (Geodesics)\nPhotons follow \nd²x^µ/dλ² + Γ^µ_νρ(dx^ν/dλ)(dx^ρ/dλ)=0. \nConstants of motion: Energy (E),\nAngular momentum (Lz), and Carter constant (Q).\n6. Numerical Integration (RK4)\nUses 4th-order Runge-Kutta with adaptive step size; smaller near photon sphere for accuracy.\n7. Relativistic Effects\nGravitational redshift, Doppler shift, and relativistic beaming (I_obs = g³ I_emit) make one side\nof the disk appear brighter.\n8. Accretion Disk Model\nFrom Shakura–Sunyaev model: T ∝ r^(-3/4), I ∝ r^(-3). Inner disk – blue, middle – yellow, outer\n– orange.\n9. Visual Phenomena Photon ring, gravitational lensing, and frame dragging cause asymmetry and multiple disk\nimages.\n10. 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@firstsalary","in_reply_to_user_id_str":null,"in_reply_to_status_id_str":null,"is_quote_status":1,"is_ai":null,"ai_score":null},{"bookmarked":false,"display_text_range":[0,55],"entities":{"hashtags":[],"symbols":[],"timestamps":[],"urls":[],"user_mentions":[]},"favorited":false,"lang":"en","quoted_status_id_str":"1984528329790406953","quoted_status_permalink":{"url":"https://t.co/Dw3j42hio0","expanded":"https://twitter.com/purusa0x6c/status/1984528329790406953","display":"x.com/purusa0x6c/sta…"},"retweeted":false,"fact_check":null,"id":"1985155687585034702","view_count":124,"bookmark_count":0,"created_at":1762132972000,"favorite_count":7,"quote_count":0,"reply_count":0,"retweet_count":0,"user_id_str":"1485557841880829953","conversation_id_str":"1985155687585034702","full_text":"do you guys need mathematical expressions for this 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of the Gödel universe\n\nThe Gödel universe is a rotating, stationary and homogeneous universe that allows the existence of closed time-like curves (CTCs).\n\nKurt Gödel, who was one of Albert Einstein's best friends in his later years, found a solution to general theory of relativity that modelled a strange, unusual and rotating universe allowing for backward time travel.\n\nThe \"time-traveler's life-line\" is a time-like curve that moves spirally through spacetime and eventually returns to its starting point.\n\nhttps://t.co/ZakvGdW0jW\n\nGödel's universe with a time-traveler's (time-like) life-line indicated. 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black holes, thought to have formed just fractions of a second after the Big Bang, might have played a crucial role in shaping the early universe by helping the first stars ignite. \n\nUnlike black holes formed from collapsing stars, these ancient objects could have emerged directly from extreme density fluctuations in the infant cosmos. \n\nNew theoretical work suggests that their gravitational pull may have drawn in surrounding matter, creating dense pockets where gas cooled and collapsed more easily, ideal conditions for star formation. \n\nIf confirmed, this idea could link the mysterious nature of dark matter with the origins of light in the universe.\n\nOne possible explanation for this larger population of black holes is that they are leftovers from a period just after the Big Bang that formed not from the collapse of massive stars but from overly dense patches of primordial gas and dust.\n\nThese \"primordial black holes\" were first postulated by Stephen Hawking over 50 years 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