general relativity - Schwarzschild solution in arbitrary dimensions

Is there any generalized Schwarzschild solution for an arbitrary number of dimensions? Is it necessary to calculate each individually, or is there a relationship between them?

Answer

In $d>4$ dimensions, the analogue of the Schwarzschild solution is $$ds^2 = - \left( 1 - \frac{2 M}{r^{d-3} } \right) dt^2 + \left( 1 - \frac{2M}{r^{d-3}} \right)^{-1} dr^2 + r^2 d \Omega_{d-2}^2$$