Energy of General Spherically Symmetric Solution in Tetrad Theory of Gravitation

TL;DR

This paper derives the most general spherically symmetric solution in a tetrad theory of gravitation, analyzes its energy using two methods, and discusses conditions for consistent energy calculations at infinity.

Contribution

It presents the most general spherically symmetric solution in a specific tetrad gravity theory and compares energy calculations from different methods.

Findings

Superpotential and Euclidean methods yield different energies unless tetrad components decay faster than 1/√r.

The energy results differ from the gravitational mass unless the tetrad's time-space components vanish sufficiently fast at infinity.

Conditions on tetrad decay rates are necessary for consistent energy definitions in this theory.

Abstract

We find the most general, spherically symmetric solution in a special class of tetrad theory of gravitation. The tetrad gives the Schwarzschild metric. The energy is calculated by the superpotential method and by the Euclidean continuation method. We find that unless the time-space components of the tetrad go to zero faster than ${1/\sqrt{r}}$ at infinity, the two methods give results different from each other, 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 ${1/\sqrt{r}}$ at infinity.