In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres. The defining characteristic of Schwarzschild chart is that the radial coordinate possesses a natural geometric interpretation in terms of the surface area and Gaussian curvature of each sphere. However, radial distances and angles are not accurately represented. These charts have many applications in metric theories of gravitation such as general relativity. They are most often used in static spherically symmetric spacetimes. In the case of general relativity, Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is static, but this is certainly not true for perfect fluids. The extension of the exterior region of the Schwarzschild vacuum solution inside the event horizon of a spherically symmetric black hole is not static inside the horizon, and the family of (spacelike) nested spheres cannot be extended inside the horizon, so the Schwarzschild chart for this solution necessarily breaks down at the horizon. (Wikipedia).
CCSS What is the Angle Addition Postulate
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Find the midpoint between two points w(–12,–7), T(–8,–4)
👉 Learn how to find the midpoint between two points. The midpoint between two points is the point halfway the line joining two given points in the coordinate plane. To find the midpoint between two points we add the x-coordinates of the two given points and divide the result by 2. This giv
From playlist Points Lines and Planes
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
CCSS What is the difference between Acute, Obtuse, Right and Straight Angles
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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What are examples of Vertical angles
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
What is General Relativity? Lesson 31:Recap & Schwarzschild effective potential
What is General Relativity? Lesson 31 Here we get back into the GR material with a recap and then we introduce the idea of the effective potential in the context of the Schwarzschild spacetime. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and d
From playlist What is General Relativity?
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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Frontiers/Controversies in Astrophysics (ASTR 160) One last key concept in Special Relativity is introduced before discussion turns again to black celestial bodies (black holes in particular) that manifest the relativistic effects students have learned about in the previous lectures. Th
From playlist Frontiers/Controversies in Astrophysics with Charles Bailyn
The Maths of General Relativity (8/8) - Summary and Applications
In this series, we build together the theory of general relativity. This eight and last video gives a summary of how one can solve a physics problem in general relativity. The video is then split into 3 examples, to illustrate the method. For more videos, subscribe to the YouTube channel
From playlist The Maths of General Relativity
Your Daily Equation #31: BLACK HOLES: And Why Time Slows Down When You Are Near One
Episode 31 #YourDailyEquation: Shortly after Einstein wrote down his new equations for gravity--his general theory of relativity--a German mathematician found the first exact solution. And within that solution physicists realized that a strange new entity was lurking: black holes. Join Bri
From playlist Your Daily Equation with Brian Greene
What’s On The Other Side Of A Black Hole?
PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Sign up for the mailing list to get episode notification
From playlist Space Time!
Lecture 4 | Topics in String Theory
(January 31, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses on the geometry of a black hole near the horizon. He describes how standard concepts from quantum physics can explain the physics that occur at this point. In the last of course of this
From playlist Lecture Collection | Topics in String Theory (Winter 2011)
Martin Taylor - The nonlinear stability of the Schwarzschild family of black holes - IPAM at UCLA
Recorded 26 October 2021. Martin Taylor of the Imperial College London presents "The nonlinear stability of the Schwarzschild family of black holes" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: I will present a theorem on the full finite codimension n
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
What is General Relativity? Lesson 74: The Schwarzschild Metric Part 2 of 2
What is General Relativity? Lesson 74: The Schwarszschild Metric Part 2 of 2 The goal of this lecture is to solve our coupled differential equations for A(\rho, t) and B(\rho, t) and thereby discover the Schwarzschild metric. This will complete our solution of the Einstein Equation in thi
From playlist What is General Relativity?
(November 12, 2012) Leonard Susskind develops the coordinate transformations used to create Penrose diagrams, and then uses them to describe the physics of black hole creation. This series is the fourth installment of a six-quarter series that explore the foundations of modern physics. In
From playlist Lecture Collection | General Relativity
What is General Relativity? Lesson 25: The Geodesics of Schwarzschild spacetime Part 4
What is General Relativity? Lesson 25: The Geodesics of Schwarzschild spacetime Part 4 In this lesson we continue to manipulate the differential equations for the trajectory of a freely falling particle in the Schwarzschild spacetime. Errata: I should point out that using the Laurent ser
From playlist What is General Relativity?
CCSS What is an angle bisector
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships