Testing no-hair theorem by quasi-periodic oscillations: thequadrupole of GRO J1655–40

Abstract

We perform an observational test of no-hair theorem usingquasi-periodic oscillations within the relativistic precession model. Twowell motivated metrics we apply are Kerr-Q and Hartle-Thorne metrics inwhich the quadrupole is the parameter that possibly encodes deviations fromthe Kerr black hole. The expressions for the quasi-periodic frequencies arederived before comparing the models with the observation. We encounter adegeneracy in constraining spin and quadrupole parameters that makes itdifficult to measure their values. In particular, we here propose a noveltest of no-hair theorem by adapting the Hartle-Thorne metric. We complement our study by doing a model comparison. We findthat there is strong evidence that Kerr black hole is the source of the central object in GROJ1655–40 given the present observational precisions.