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

TL;DR

This paper constructs multipole moments for stationary spacetimes in higher-order gravity theories, explores their recurrence relations for Kerr-Newman metrics, and tests no-hair relations using galactic microquasar oscillation data.

Contribution

It extends the definition of multipole moments to higher-order gravity theories and investigates their implications for black hole no-hair relations in astrophysical observations.

Findings

Kerr-Newman moments follow similar recurrence relations as in GR.

Microquasar data constrains black hole spins and charges in $f(R)$ gravity.

Potential preservation of no-hair relations in $f(R)$ theories despite breakdown in GR.

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.