Effect of a variable cosmological constant on black hole quasinormal modes

TL;DR

This paper investigates how a variable cosmological constant affects black hole quasinormal modes, proposing that these effects could, in principle, track cosmological evolution but are practically undetectable.

Contribution

It introduces four models of a time-dependent cosmological constant and analyzes their impact on black hole quasinormal modes, highlighting the negligible observational effects.

Findings

Frequency shifts grow with black hole mass squared

Variations in the cosmological constant cause minute frequency shifts

Detection prospects of these shifts are practically nonexistent

Abstract

Many different cosmological models have been proposed to address the cosmological constant problem and the coincidence problem. We compare here four different models that can be used to describe an effective (time-dependent) cosmological constant $\Lambda(z)$. A numerical analysis of the $\Lambda(z)$ evolution obtained for each model shows that it can be used for distinguishing between all four models. We calculate next the $\omega(\Lambda)$ frequencies for quasinormal modes of gravitational perturbations of Schwarzschild-de Sitter black holes at different redshifts. Considering that the variation of $\Lambda$ happens on cosmological timescales, the combined $\omega(\Lambda(z))$ could be used in principle to track the evolution of the cosmological constant. We quantify the resulting minute frequency shift in the quasinormal mode frequencies and show that the relative frequency shift grows as $M^2$. However, even in a most optimistic scenario with an extremely high mass supermassive black hole there is no prospect for the detection of this effect.