Pathology of the Unified Dark Sectors in Modified General Relativity

TL;DR

This paper analyzes the stability of black hole solutions in Modified General Relativity, revealing a fundamental instability in the polar perturbation sector due to a coupling that diverges at large distances, questioning the theory's viability.

Contribution

It provides a gauge-invariant stability analysis of MGR black holes, identifying a critical infrared instability caused by the coupling of metric fluctuations to the line element field.

Findings

Polar perturbations exhibit a divergence at large distances.

Axial perturbations remain stable.

The instability is due to a coupling mechanism specific to MGR.

Abstract

This paper presents a comprehensive stability analysis of the black hole solution within Modified General Relativity (MGR), a theory proposing a unified geometric description of dark matter (DM) and dark energy (DE). A rigorous gauge-invariant formalism is employed to analyze gravitational perturbations of the extended Schwarzschild metric. The central finding is a critical pathology within the polar perturbation sector, where metric fluctuations couple to the theory's fundamental line element field. This coupling is governed by a factor that, while well-behaved at the horizon, diverges powerfully in the far-field limit as a direct consequence of the theory's non-asymptotically flat nature. This indicates a strong infrared instability that overwhelms perturbations at large distances. In stark contrast, the axial perturbation sector is found to be completely stable. This dichotomy proves that the instability is not inherent to the background metric but is specifically generated by the novel coupling mechanism encoding MGR's unified dark sectors. The results reveal a fundamental strong-coupling problem within the MGR framework, challenging its physical viability as an alternative to Einstein's General Relativity (EGR).