Effect of signature change in NGR

TL;DR

This paper investigates how changing the signature in the field equations of new general relativity affects solutions, revealing differences in solutions and energy content, and suggesting potential for new physics.

Contribution

It introduces the effect of signature change in NGR field equations, leading to new solutions and insights into the theory's physical implications.

Findings

Signature change yields different solutions from Schwarzschild.

Energy content varies between solutions with and without signature change.

Signature change may lead to new physical phenomena.

Abstract

The field equations of the new general relativity (NGR) have been applied to an absolute parallelism space having three unknown functions of the radial coordinate. The field equations have been solved using two different schemes. In the first scheme, we used the conventional procedure used in orthodox general relativity. In the second scheme, we examined the effect of signature change. The latter scheme gives a solution which is different from the Schwarzschild one. In both methods we find solution of the field equations under the same constraint imposed on the parameters of the theory. We also calculated the energy associated with the solutions in the two cases using the superpotential method. We found that the energetic content of one of the solutions is different from that of the other. A comparison between the two solutions obtained in the present work and a third one obtained by Hayashi and Shirafuji (1979) shows that the change of the signature may give rise to new physics.