A special exact spherically symmetric solution in f(T) gravity theories

TL;DR

This paper derives a special exact vacuum solution in f(T) gravity using a non-diagonal spherically symmetric tetrad, revealing insights into gravitational mass and scalar torsion in modified gravity theories.

Contribution

It presents a novel exact spherically symmetric solution in f(T) gravity with a detailed analysis of its physical properties and energy characteristics.

Findings

Scalar torsion vanishes for the solution

Energy calculation relates to gravitational mass

Solution involves a constant of integration

Abstract

A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$, is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is obtained. The scalar torsion related to this special solution vanishes. To understand the physical meaning of the constant of integration we calculate the energy associated with this solution and show how it is related to the gravitational mass of the system.