# Schwarzschild’s Solution and Black Holes

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## Abstract

In Chap. 14 we showed that the exterior Schwarzschild solution of Einstein’s equation describes the gravitational field outside a *static* spherical mass with constant mass density. This solution has the peculiar characteristic that some components of the metric tensor became infinite at the *Schwarzschild radius* \(r_{s}=2m\) and at \(r=0\). The nature and meaning of this behavior was not quite understood at the time of its discovery (1916), although the bending of light and the redshift of clocks in a gravitational field were phenomena already acquired.

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