Distributional energy-momentum densities of Schwarzschild space-time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density (T) over tilde(mu)(nu)(x) of the gravitational source and the gravitational energy-momentum pseudo-tenser density (t) over tilde(mu)(nu) have the expressions (T) over tilde(mu)(nu)(x) = Mc(2) delta(mu)(0) delta(0)(nu)delta((3))(x) and (t) over tilde(mu)(nu) = 0, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like delta((3))(x)/r(3) and [delta((3))(x)](2), as well as other terms, which are singular at x = 0. It is pointed out that the well-known expression R-rho sigma mu nu({})R-rho sigma mu nu({}) = 48G(2)M(2)/c(4)r(6) is not correct, if we define 1/r(6) (sic) lim(epsilon-->0)1//(r(2) + epsilon(2))(3).