Difference between revisions of "Schwarzschild black hole"
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Revision as of 08:51, 17 June 2012
The spherically symmetric solution of Einstein's equations in vacuum for the spacetime metric has the form \cite{Schw} \begin{align}\label{Schw} ds^{2}=h(r)\,dt^2-h^{-1}(r)\,dr^2-r^2 d\Omega^{2}, &\qquad\mbox{where}\quad h(r)=1-\frac{r_g}{r};\quad r_{g}=\frac{2GM}{c^{2}};\\ d\Omega^{2}=d\theta^{2}+\sin^{2}\theta\, d\varphi^{2}&\;\text{-- metric of unit sphere.}\nonumber \end{align} The Birkhoff's theorem (1923) \cite{Birkhoff,Jebsen} states, that this solution is unique up to coordinate transformations. The quantity $r_g$ is called the Schwarzschild radius, or gravitational radius, $M$ is the mass of the central body or black hole.
Contents
Simple problems
Problem 1.
problem formulation
problem solution
Problem 2.
problem formulation
problem solution
Problem 3.
problem formulation
problem solution
Problem 4.
problem formulation
problem solution
Problem 5.
problem formulation
problem solution
Symmetries and integrals of motion
Problem 6.
problem formulation
problem solution
Problem 7.
problem formulation
problem solution
Problem 8.
problem formulation
problem solution
Problem 9.
problem formulation
problem solution
Problem 10.
problem formulation
problem solution
Problem 11.
problem formulation
problem solution
Problem 12.
problem formulation
problem solution
