The Schwarzschild Solution

Einstein’s field equations are nonlinear and are therefore very complicated, and it is difficult to get accurate solutions of them. There is, however, one special case which can be solved without too much trouble, namely, the static spherically symmetric field produced by a spherically mass M at rest. Schwarzschild first found this in 1916, and this solution has played a major role in the early development of general relativity and is even today regarded as a solution of fundamental importance. In the Newtonian gravitation the solution of this problem is described by a gravitational potential Φ = GM/r, where M is the gravitational mass of the source distribution and r is the radius coordinate from the center of the mass distribution. The Schwarzschild solution describes the general relativistic analog of the Newtonian solution.