Home Page Overview Site Map Index Appendix Illustration About Contact Update FAQ

Relativity, Cosmology, and Time

Schwarzschild's Solution and Black Hole

The equations of metric tensors can be solved exactly for the case of a centrally symmetric field in vacuum with mass M at the center. In terms of spherical coordinates and ct, the "world line" has the curvilinear form :

ds2 = (1 - 2GM/c2r) c2dt2 - dr2 / (1 - 2GM/c2r) - r2 (sin2 d2 + d2) ---------- (13)

This is the celebrated Schwarzschild solution. The integration constant often referred to as the Schwarzschild's radius (or event horizon) rs = 2GM/c2 appears in the formula in order to relate to Newton's inverse square law, otherwise it is rather arbitrary. Some special properties about this metric are listed in the followings :