Mass-energy in static gravitational fields

The mass-energy equation in static gravitational fields is shown to be E = g44mc2, which agrees with the expression E = m0c2(dxsup(μ)/ds)xisub(μ) for the energy in a gravitational field possessing a timelike Killing vector xi. For the Schwarzschild field this leads to Esub(s) approximately equal to m0c2 + 1/2m0upsilon2 - km0M/r. For the Reissner-Nordstroem field an additional term describing the interaction between the mass and the charge is found to be 2πkm0Q2/c2r2. In the Kerr-Newman case more terms are found due to the central rotating gravitating mass. (author)