Non-vacuum black holes in new general relativity

TL;DR

This study probes whether New General Relativity (NGR) can host physically meaningful, non-trivial black holes by examining static, spherically symmetric spacetimes with horizon structures. Using a fully covariant teleparallel formulation, the authors analyze both vacuum and non-vacuum cases via perturbative LH (local horizon) techniques, enforcing energy-momentum conservation and the symmetric/antisymmetric field equations. They classify the NGR parameter space, impose ghost-free and Newtonian-limit requirements, and perform a meticulous leading- and next-to-leading-order analysis of the field equations for multiple branches. The main finding is that non-TEGR branches either reduce to TEGR, violate essential physical constraints (ghosts, lack of a Newtonian limit, absence of propagating spin-2 modes), or fail to sustain a consistent horizon geometry, thus yielding no physically acceptable non-trivial black holes in NGR. Consequently, within the perturbative approach adopted, NGR does not extend black-hole physics beyond TEGR and GR in a physically meaningful way.

Abstract

New general relativity (NGR) possesses a region in the \((c_{a},c_{v},c_{t})\)-parameter space corresponding to physically acceptable models. However, when solving the field equations for vacuum and non--vacuum static and spherically symmetric configurations under the assumption of the existence of a local black hole horizon, we find that the mere existence of such solutions imposes algebraic constraints that fix the parameters to values associated with known pathological models. As a consequence, we conclude that NGR is unable to describe physically meaningful non-trivial black holes.