Self-dual Lorentzian Wormholes and Energy in Teleparallel Theory of Gravity

TL;DR

This paper presents new self-dual Lorentzian wormhole solutions in teleparallel gravity, analyzing their properties and energy content, revealing that the energy is either equal to the mass parameter or twice the mass, independent of certain solution parameters.

Contribution

It introduces a class of self-dual Lorentzian wormholes in teleparallel gravity characterized by two parameters, with a detailed energy analysis showing parameter independence.

Findings

Energy of wormholes is either m or 2m.

Solutions include the Schwarzschild black hole as a special case.

The wormholes are characterized by two parameters but share the same metric.

Abstract

Two spherically symmetric, static Lorentzian wormholes are obtained in tetrad theory of gravitation as a solution of the equation $\rho=\rho_t=0$, where $\rho=T_{ij}u^iu^j, \rho_t=(T_{ij}-{1/2}Tg_{ij})u^iu^j$ and $u^iu_i=-1$. This equation characterizes a class of spacetime which are "self-dual" (in the sense of electrogravity duality). The obtained solutions are characterized by two-parameters $k_1, k_2$ and have a common property that they reproduce the same metric spacetime. This metric is the static Lorentzian wormhole and it includes the Schwarzschild black hole. Calculating the energy content of these tetrad fields using the {\it superpotential method given by M{\o}ller in the context of teleparallel spacetime} we find that $E=m$ or $2m$ which does not depend on the two parameters $k_1$ and $k_2$ characterize the wormhole.