Veiled Singularities in Einstein-Weyl Gravity: Stability and Physical Interpretation of Horizonless Solutions

TL;DR

This paper demonstrates that certain horizonless naked singularities in Einstein-Weyl gravity are linearly stable under tensor perturbations, suggesting they could serve as stable, black hole mimickers in higher-derivative gravity theories.

Contribution

It provides the first stability analysis of veiled singularities in Einstein-Weyl gravity, showing their potential as stable, horizonless solutions unlike in General Relativity.

Findings

Naked singularities are linearly stable under tensor perturbations.

Perturbation modes decay with oscillatory tails, indicating stability.

These solutions are phenomenologically similar to black holes and could be observationally concealed.

Abstract

We investigate a class of horizonless solutions in Einstein-Weyl gravity, corresponding to the so-called attractive naked singularities of the (-2,2) type. In contrast to General Relativity, where naked singularities are generically unstable and excluded by the cosmic censorship conjecture, we show that these configurations are linearly stable under tensor perturbations. By numerically evolving the perturbation equations in the time domain, we find that all modes decay with characteristic oscillatory tails, a behavior consistent with the dynamics of massive field perturbations in quadratic gravity. This establishes that attractive naked singularities in Einstein-Weyl gravity are dynamically stable and can persist as stationary configurations. We argue that these horizonless configurations are observationally concealed, and therefore we refer to them as veiled singularities. Their stability and phenomenological similarity to black holes suggest that they may represent viable horizonless alternatives in higher-derivative theories of gravity, offering a novel perspective on the interplay between singularity resolution, stability, and effective field dynamics beyond Einstein's theory.