Bayesian analysis of analog gravity systems with the Rezzolla-Zhidenko metric

TL;DR

This paper explores how laboratory analog gravity systems can be used to infer black hole metrics by analyzing perturbations with Bayesian methods, offering a new approach beyond traditional quasi-normal mode analysis.

Contribution

It introduces a Bayesian framework to analyze perturbations in analog gravity experiments using the Rezzolla-Zhidenko metric, enabling comprehensive inference of black hole-like spacetimes.

Findings

Bayesian analysis can constrain regions of the effective spacetime.

The method models the entire signal, including prompt response and tails.

It does not depend on start/end times or mode count assumptions.

Abstract

Analog gravity systems have the unique opportunity to probe theoretical aspects of black hole physics in a controlled laboratory environment that one cannot easily observe for astrophysical black holes. In this work, we address the question of whether one could use controlled initial perturbations to excite the black hole ringdown and infer the effective black hole metric. Using a theory-agnostic ansatz for the effective metric described by the Rezzolla-Zhidenko metric and evolving perturbations on that background, we quantify with Bayesian analysis what regions of the effective spacetime could be constrained in experiments. In contrast to standard ringdown analyses based on quasi-normal mode extraction, a laboratory-controlled setup, in combination with our framework, allows one to model the entire signal, including the prompt response and possible effects of late-time tails. Therefore, it has the intriguing advantage of not relying on start and end times when the superposition of quasi-normal modes is a good signal approximation. It also avoids the non-trivial question of how many modes are present. We demonstrate that this approach is feasible in principle and discuss opportunities beyond this study.