On non-vacuum black holes in new general relativity

TL;DR

This paper investigates static, spherically symmetric black hole solutions in new general relativity, revealing that physically meaningful black holes only exist in models equivalent to teleparallel gravity, with other parameter choices leading to pathologies.

Contribution

It demonstrates that within NGR, only models equivalent to teleparallel gravity admit physically acceptable black hole solutions, highlighting limitations of the theory.

Findings

Existence of black holes constrains NGR parameters to pathological regions.

Regular horizon geometries are only found in models equivalent to teleparallel gravity.

NGR generally does not support physically meaningful non-trivial black holes.

Abstract

New general relativity (NGR) is a torsion-based modification of general relativity whose Lagrangian depends on three free parameters, $(c_{a}, c_{v}, c_{t})$. A subset of the parameter space is physically admissible, namely that which simultaneously ensures ghost-freedom, propagation of a spin-2 mode, and a consistent Newtonian limit. In this work we analyze static and spherically symmetric configurations in NGR, both in vacuum and in the presence of a perfect fluid and an electromagnetic field, under the assumption of the existence of a local black-hole horizon. We find that the mere existence of such configurations forces the free parameters into regions associated with known pathological models: theories that either contain ghost instabilities, do not propagate a spin-2 mode, or lack a Newtonian limit. The remaining geometries are regular at the horizon, so the obstruction is not a breakdown of the geometry but a breakdown of the underlying theory. We therefore conclude that, within the class of models examined, NGR does not admit physically meaningful non-trivial black holes distinct from those of the teleparallel equivalent of general relativity.