Hello everybody! I have some questions concerning the structure of the Schwarzschild metric, which is given by(adsbygoogle = window.adsbygoogle || []).push({});

$$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$

where we set $c=1$. I would like to know the following: \\

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1. Why is it reasonable to consider $M$ as the mass of the black hole? What is the motivation behind this? \\

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2. What are the geodesics in the Schwarzschild solution? Is there any good way to visualize them all at once?

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Every answer would be appreciated

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# Questions about the Schwarzschild metric

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