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Tensors and Relativity: Chapter 8

The Schwarzschild solution

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For static vacuum fields, the field equations reduce to

eqnarray1027

The second of these equations is equivalent to

equation1029

Under the substituting tex2html_wrap_inline1276 , the third equation transforms into the differential equation

equation1031

whose general solution is

equation1033

where 2GM is a constant of integration. Thus, the spherically symmetric vacuum solution, first found in 1916 by Schwartzschild, has the line element

equation1035

 

figure588

Figure 8.1: K. Schwarzschild


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