: Please show me how Schwarzschild derived Rs=2GM/c^2. Thank you.

Swartzchild derived the space-time geometry for a nonrotating noncharged black hole contained in the equation ds2 = (1 - Rs/r)dct2 - dr2/(1 - Rs/r) - r2(dq2 + sin2qdf2)

The sight its linked to shows his derivation. Rs is an integration constant picked up along the path of the derivation. The relativisticaly correct way to show that it is 2GM/c2 is to show that that choice for the integration constant leads to Newtonian behavior in a Newtonian limit. The easiest way to do this is to show that Rs = 2GM/c2 gives the correct Kepler's third law for circular motion. Otherwise its luck that a nonrelativistic derivation will also give the relativistic answer.

• http://hometown.aol.com//zephcochrane/WarpDrives.html