Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology

TL;DR

This paper explores spherically symmetric vacuum solutions in a modified teleparallel gravity theory, analyzing their phenomenology and observational signatures, and comparing them with classical General Relativity predictions.

Contribution

It derives new vacuum solutions in 1-parameter New General Relativity and examines their observational implications, extending understanding of torsion-based gravity theories.

Findings

Three distinct vacuum solution branches identified

Photon sphere and classical tests analyzed in the new solutions

Observational effects on accretion disks and shadows discussed

Abstract

In this work, we study spherically symmetric vacuum solutions in 1-parameter New General Relativity (NGR), a specific theory in teleparallel gravity which is constructed from the three possible quadratic scalars obtained from torsion with arbitrary coefficients satisfying the requirements for the absence of ghosts. In this class of modified theories of gravity, the observable effects of gravity result from the torsion rather than the curvature of the spacetime. Unlike in GR, where the fundamental quantity is the metric from which the Levi-Civita connection is derived, in teleparallel theories of gravity the fundamental variable is the tetrad, from which one constructs the metric and the teleparallel connection. We consider the most general tetrad for spherical symmetry and we derive the corresponding field equations. Under adequate assumptions, we find three different branches of vacuum solutions and discuss their associated phenomenology. In particular, we analyze the photon sphere, the classical tests of GR such as the light deflection, the Shapiro delay, and the perihelion shift, and also the Komar mass, while providing a detailed comparison with their Schwarzschild spacetime counterparts. Finally, we analyze how the observational imprints from accretion disks and shadows are affected in comparison with their GR counterparts, and conclude that the free parameters of the model might induce additional attractive or repulsive effects to the propagation of photons, depending on their values.