On the physical viability of black hole solutions in Einsteinian Cubic Gravity and its generalisations

TL;DR

This paper analyzes the stability and physical viability of black hole solutions in Einsteinian Cubic Gravity and its extensions, revealing generic pathologies that challenge their use as fundamental theories but not as perturbative corrections.

Contribution

It demonstrates that black holes in Einsteinian Cubic Gravity exhibit pathological behaviors due to degeneracies in their perturbation equations, questioning their viability as fundamental theories.

Findings

Pathologies are linked to degenerate principal parts in perturbation equations.

These issues are generic for cubic and higher-order theories with similar spectra.

The problems are not present when these theories are treated as perturbative corrections to GR.

Abstract

In this note, we discuss the pathological nature of black holes in Einsteinian Cubic gravity and its extensions. We compute the equations for the odd perturbations and show how spherically symmetric solutions that asymptotically approach a maximally symmetric space (Minkowski, de Sitter or anti-de Sitter) are associated to having an asymptotically degenerate principal part of the equations. We use these results to argue that the encountered problems will be generic for any other cubic or higher-order with a reduced linear spectrum around maximally symmetric spaces except the well-known healthy case of $f(R)$. We highlight that these pathologies are only alarming when the theory is regarded as a complete theory, but not when considered as a perturbative correction to GR (as in e.g. the effective field theory framework) since the the low-energy physics remains safe from them. Our results thus cast doubts on possible resolutions of the singularities or non-perturbative effects on horizons based on these theories.