Interior Schwarzschild metric

General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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In Einstein's theory of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid (implying that density is constant throughout the body) and has zero pressure at the surface. This is a static solution, meaning that it does not change over time. It was discovered by Karl Schwarzschild in 1916, who earlier had found the exterior Schwarzschild metric.^[1]