Wormhole solution and Energy in Teleparallel Theory of Gravity

TL;DR

This paper derives a spherically symmetric Lorentzian wormhole solution in teleparallel gravity, explores its properties, and calculates the associated gravitational energy, revealing dependence on an arbitrary function but not on the wormhole parameters.

Contribution

It presents a new exact wormhole solution in teleparallel gravity characterized by two parameters and an arbitrary function, and analyzes its energy content.

Findings

The solution includes Schwarzschild black hole and naked singularities.

Energy calculation depends on the arbitrary function, not on wormhole parameters.

Regularized energy expression yields parameter-independent energy.

Abstract

An exact solution is obtained in the tetrad theory of gravitation. This solution is characterized by two-parameters $k_1, k_2$ of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation $\rho=\rho_t=0$ with $\rho=T_{i,j}u^iu^j$, $\rho_t=(T_{ij}-\displaystyle{1 \over 2}Tg_{ij}) u^iu^j$ where $u^iu_i=-1$. From this solution which contains an arbitrary function we can generates the other two solutions obtained before. The associated metric of this spacetime is a static Lorentzian wormhole and it includes the Schwarzschild black hole, a family of naked singularity and a disjoint family of Lorentzian wormholes. Calculate the energy content of this tetrad field using the gravitational energy-momentum given by M{\o}ller in teleparallel spacetime we find that the resulting form depends on the arbitrary function and does not depend on the two parameters $k_1$ and $k_2$ characterize the wormhole. Using the regularized expression of the gravitational energy-momentum we get the value of energy does not depend on the arbitrary function.