Probing the warped vacuum geometry around a Kerr black hole by quasi-periodic oscillations

TL;DR

This paper explores how quasi-periodic oscillations around a Kerr black hole with a cosmological constant can reveal details of the warped vacuum geometry, but finds the classical Kerr model is statistically preferred.

Contribution

It introduces a new extended Kerr-de Sitter black hole solution and applies Bayesian analysis to compare it with the classical Kerr metric using QPO data.

Findings

Kerr metric is statistically favored over the extended solution.

The cosmological constant parameter is degenerate with other parameters.

QPO frequencies are calculated within the new black hole geometry.

Abstract

We investigate quasi-periodic oscillations (QPOs) in the context of a new rotating black hole solution that incorporates a cosmological constant. Recent work by the authors in \cite{Ovalle:2022eqb} interpreted the cosmological constant, denoted as $\Lambda$, as a form of vacuum energy and employed a gravitational decoupling approach to derive an extended Kerr-de Sitter black hole solution, which is geometrically richer than the classical case. In this study, we derive the expressions for timelike circular geodesics within this solution and, using a relativistic precision model, calculate the corresponding frequencies of the QPOs. To constrain our model, we apply Bayesian formalism, utilizing data from three well-known microquasars: GRO 1655-40, XTE 1550-564, and GRS 1915+105. Our analysis reveals that$\Lambda$ is degenerate and correlated with other parameters. Finally, we perform a Bayesian model comparison with the Kerr metric and find that the Kerr metric is favored among the models considered.