Testing modified gravity and no-hair relations for the Kerr-Newman metric through quasi-periodic oscillations of galactic microquasars

Abstract

We construct multipole moments for stationary, asymptotically flat, spacetime solutions to higher-order curvature theories of gravity. The moments are defined using $3+1$ techniques involving timelike Killing vector constructions as in the classic papers by Geroch and Hansen. Using the fact that the Kerr-Newman metric is a vacuum solution to a particular class of $f(R)$ theories of gravity, we compute all its moments, and find that they admit recurrence relations similar to those for the Kerr solution in general relativity. It has been proposed previously that modelling the measured frequencies of quasi-periodic oscillations from galactic microquasars enables experimental tests of the no-hair theorem. We explore the possibility that, even if the no-hair relation is found to break down in the context of general relativity, there may be an $f(R)$ counterpart that is preserved. We apply the results to the microquasars GRS $1915$+$105$ and GRO J$1655$-$40$ using the diskoseismology and kinematic resonance models, and constrain the spins and `charges' [which are not really electric charges in the $f(R)$ context] of their black holes.

14 pages, 5 figures; Accepted for publication in PRD

References in corpus (13)

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• How to observe a non-Kerr spacetime
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• Multipole moments in scalar-tensor theory of gravity
• Diskoseismology and QPOs Confront Black Hole Spin
• Explicit multipole moments of stationary axisymmetric spacetimes
• Tracing the geometry around a massive, axisymmetric body to measure, through gravitational waves, its mass moments and electromagnetic moments
• Confronting models for the high-frequency QPOs with Lense-Thirring precession
• Measuring mass moments and electromagnetic moments of a massive, axisymmetric body, through gravitational waves
• Multipole moments of bumpy black holes

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• Testing gravity of a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories by quasi-periodic oscillations
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