Tensors and Relativity: Chapter 8
The Schwarzschild solution
Next: General discussion of the Up: Title page Previous: The vacuum field equations
For static vacuum fields, the field equations reduce to
The second of these equations is equivalent to
Under the substituting , the third equation transforms into the differential equation
whose general solution is
where 2GM is a constant of integration. Thus, the spherically symmetric vacuum solution, first found in 1916 by Schwartzschild, has the line element

Figure 8.1: K. Schwarzschild