  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 $\tilde
T_\mu^{\nu}(x)$ of the gravitational source and the gravitational
energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions
$\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and
$\tilde t_\mu^{\nu}=0$, 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 $1/r^6 = \lim_{\epsilon\to
0}1/(r^2+\epsilon^2)^3$.}
