- #1
nick41
- 4
- 0
Hello everybody! I have some questions concerning the structure of the Schwarzschild metric, which is given by
$$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$
where we set $c=1$. I would like to know the following: \\
\\
1. Why is it reasonable to consider $M$ as the mass of the black hole? What is the motivation behind this? \\
\\
2. What are the geodesics in the Schwarzschild solution? Is there any good way to visualize them all at once?
\\
\\
Every answer would be appreciated
$$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$
where we set $c=1$. I would like to know the following: \\
\\
1. Why is it reasonable to consider $M$ as the mass of the black hole? What is the motivation behind this? \\
\\
2. What are the geodesics in the Schwarzschild solution? Is there any good way to visualize them all at once?
\\
\\
Every answer would be appreciated