On Lynden-Bell and Katz's definition of gravitational field energy

The covariant definition of gravitational field energy given by Lynden-Bell and Katz is expressed in terms of Israel's theory of surface layers in general relativity. In this way an expression, valid for arbitrary radial coordinates, of the gravitational field energy in a static, spherically symmetric space-time, is deduced. This expression is applied to the Schwarschild and Reissner-Nordström space-times, and leads here to the same results as those given by Einstein's pseudotensor expression in isotropic coordinates.