Exact solutions in general relativity
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916, and around the same time independently by , who published his more complete and modern-looking discussion four months after Schwarzschild. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum. A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass. The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon, which is situated at the Schwarzschild radius, often called the radius of a black hole. The boundary is not a physical surface, and a person who fell through the event horizon (before being torn apart by tidal forces), would not notice any physical surface at that position; it is a mathematical surface which is significant in determining the black hole's properties. Any non-rotating and non-charged mass that is smaller than its Schwarzschild radius forms a black hole. The solution of the Einstein field equations is valid for any mass M, so in principle (according to general relativity theory) a Schwarzschild black hole of any mass could exist if conditions became sufficiently favorable to allow for its formation. In the vicinity of a Schwarschild black hole, space curves so much that even light rays are deflected, and very nearby light can be deflected so much that it travels several times around the black hole. (Wikipedia).
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?
The Meaning Behind the Black Hole Equation | Physics Made Easy
The Schwarzschild Metric is very often used to describe nonrotating, uncharged, black holes (as well as other gravitational bodies) and the effect that they have on the spacetime around them. Hey guys, I'm back with a video that I kinda threw together, because I'm on holiday at the moment
From playlist Relativity by Parth G
What is General Relativity? Lesson 73: Solving for the Schwarzschild Metric Part 1 of 2
What is General Relativity? Lesson 73: Solving for the Schwarzschild metric Part 1 of 2 This lesson will discover the coupled non-linear differential equations which define the Schwarzschild spacetime. This process is tedious, but we show exactly how the calculation is done and execute en
From playlist What is General Relativity?
19/11/2015 - Gustav Holzegel - The Linear Stability of the Schwarzschild Solution
The Linear Stability of the Schwarzschild Solution Under Gravitational Perturbations https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-g-holzegel.pdf
From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
What is General Relativity? Lesson 23: The Geodesics of Schwarzschild spacetime Part 2
What is General Relativity? Lesson 23: The Geodesics of Schwarzschild spacetime Part 2 Check out the forums at http://xylyxylyx.freeforums.net/ and the Patreon page at https://www.patreon.com/XYLYXYLYX
From playlist What is General Relativity?
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From playlist What is General Relativity?
The Schwarz Lemma -- Complex Analysis
Part 1 -- The Maximum Principle: https://youtu.be/T_Msrljdtm4 Part 3 -- Liouville's theorem: https://www.youtube.com/watch?v=fLnRDhhzWKQ In today's video, we want to take a look at the Schwarz lemma — this is a monumental result in the subject of one complex variable, and has lead to many
From playlist Complex Analysis
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What is General Relativity? Lesson 72: Schwarzschild Solution - the Setup In this lesson we are going to set up the mathematical problem we are solving and relate that problem to physics. In preparation for this we need to understand what a spherically symmetric metric must look like, and
From playlist What is General Relativity?
17/11/2015 - Jérémie Szeftel - Remarks on the nonlinear stability of Schwarzschild
https://philippelefloch.files.wordpress.com/2015/11/ihp-2015-jc3a9rc3a9mieszeftel.pdf
From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
Your Daily Equation #31: BLACK HOLES: And Why Time Slows Down When You Are Near One
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From playlist Your Daily Equation with Brian Greene
What is General Relativity? Lesson 31:Recap & Schwarzschild effective potential
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From playlist What is General Relativity?
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
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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
13. Stellar Mass Black Holes (cont.)
Frontiers/Controversies in Astrophysics (ASTR 160) Class begins with clarification of equations from the previous lecture. Four post-Newtonian gravitational effects are introduced and discussed in detail. The first of these is the so-called Perihelion Precession, which occurs when the m
From playlist Frontiers/Controversies in Astrophysics with Charles Bailyn
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
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From playlist Lecture Collection | Topics in String Theory (Winter 2011)
What is General Relativity? Lesson 22: The geodesics of the Schwarzschild spacetime
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From playlist What is General Relativity?
Why Black Holes MUST Be Disordered - Entropy of a Black Hole, Thermodynamics & Physics
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From playlist Relativity by Parth G