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## Main Question or Discussion Point

In 1916 Schwarzschild wrote down his famous metric to solve (or re-solve using a polar coordinate system) the precession of the perihelion of Mercury. The curvature of spacetime described by the Metric is for any non-rotating spherically symmetric mass.

[tex]ds^2 = -(1-\frac{2M}{r})dt^2 + (1-\frac{2M}{r})^{-1}dr^2 + r^2(d\theta^2+sin^2\theta d\phi^2)[/tex]

Does this imply there is a black hole at the center of the Sun, the Earth etc?

[tex]ds^2 = -(1-\frac{2M}{r})dt^2 + (1-\frac{2M}{r})^{-1}dr^2 + r^2(d\theta^2+sin^2\theta d\phi^2)[/tex]

Does this imply there is a black hole at the center of the Sun, the Earth etc?