Testing No-Hair Theorem by Quasi-Periodic Oscillations: the quadrupole of GRO J1655$-$40

TL;DR

This paper tests the no-hair theorem by analyzing quasi-periodic oscillations in GRO J1655-40 using relativistic models, finding that current data supports the Kerr black hole description.

Contribution

It introduces a novel test of the no-hair theorem using the Hartle-Thorne metric and discusses the challenges in constraining spin and quadrupole parameters.

Findings

Kerr black hole model fits observational data well.

Degeneracy exists in constraining spin and quadrupole.

Current observational precision supports the Kerr description.

Abstract

We perform an observational test of no-hair theorem using quasi-periodic oscillations within the relativistic precession model. Two well motivated metrics we apply are Kerr-Q and Hartle-Thorne metrics in which the quadrupole is the parameter that possibly encodes deviations from the Kerr black hole. The expressions for the quasi-periodic frequencies are derived before comparing the models with the observation. We encounter a degeneracy in constraining spin and quadrupole parameters that makes it difficult to measure their values. In particular, we here propose a novel test of no-hair theorem by adapting the Hartle-Thorne metric. It turns out that a Kerr black hole is a good description of the central object in GRO J1655$-$40 given the present observational precisions.