Energy of general spherically symmetric solution in the tetrad theory of gravitation

Takeshi Shirafuji, Saitama University
Gamal G.L. Nashed, Saitama University
Kenji Hayashi, Kitasato University

Abstract

We find the most general spherically symmetric solution in a special class of the tetrad theory of gravitation. The tetrad gives the Schwarzschild metric. The energy is calculated using both the superpotential method and the Euclidean continuation method. We find that unless the time-space components of the tetrad go to zero faster than 1/√r at infinity, the two methods give different results and that these results differ from the gravitational mass of the central gravitating body. This fact implies that the time-space components of the tetrad describing an isolated spherical body must vanish faster than 1/√r at infinity.