General Teleparallel Modifications of Schwarzschild Geometry

TL;DR

This paper explores modifications to Schwarzschild geometry within teleparallel gravity theories, analyzing spherical symmetry, deriving solutions, and assessing phenomenological effects like light deflection and perihelion shift.

Contribution

It introduces a generalized teleparallel gravity framework based on scalar torsion invariants and provides analytical and perturbative solutions around Schwarzschild geometry.

Findings

Derived exact solutions for conformal teleparallel gravity.

Computed phenomenological corrections to GR predictions.

Identified dependence of effects on three model parameters.

Abstract

Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary function of the five possible scalars constructed from the irreducible parts of torsion. This theory is a generalisation of the so-called New General Relativity theory. We find that only two scalars are different to zero in spherical symmetry and we solve the corresponding field equations analytically for conformal Teleparallel gravity, and then perturbatively around Schwarzschild geometry for the general perturbative theory around GR. Finally, we compute phenomenological effects from the perturbed solutions such as the photon sphere, perihelion shift, Shapiro delay, and the light deflection. We find their correspondent correction to the standard GR contribution and their dependence on the three model parameters.