Inside an event horizon, write g_00 and g_11 of the Schwarzschild metric, as S and -1/S, with S = (2m-r)/r . Outside, a minus sign gives the usual form. My goal was to evaluate integrals of proper distance from the very center. For the interior result I find an integral from CRC tables useful with two linear transforms, so I will compose the calculus material. For the exterior result, Wolfram came to my rescue!!!