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Schwarzschild Metric

A specific metric describing the spacetime around a non-rotating, spherically symmetric mass, fundamental for black hole solutions.

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The statement of the theorem

The Schwarzschild metric

g_{\mu\nu}

describes the spacetime around a non-rotating, spherically symmetric mass

M

. In standard coordinates

(t, r, \theta, \phi)

, the line element

ds^2

is given by:\n\n

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

\n\nHere,

G

is the gravitational constant,

c

is the speed of light, and

r

is the radial coordinate.

Source: Wikipedia