Black Hole Multipoles in Higher-Derivative Gravity

TL;DR

This paper investigates how higher-derivative modifications to Einstein gravity affect the multipole moments of rotating black holes, providing new analytical expressions and exploring their implications for gravitational wave observations.

Contribution

It extends the definition and calculation of black hole multipoles to higher-derivative gravity theories, including closed-form solutions and relations between multipole corrections.

Findings

Derived multipole moments for higher-derivative Kerr black holes.

Identified relations between parity-odd and parity-preserving multipole corrections.

Discussed potential observational signatures in gravitational wave data.

Abstract

We consider a broad family of higher-derivative extensions of four-dimensional Einstein gravity and study the multipole moments of rotating black holes therein. We carefully show that the various definitions of multipoles carry over from general relativity, and compute these multipoles for higher-derivative Kerr using the ACMC expansion formalism. We obtain the mass $M_{n}$ and current $S_{n}$ multipoles as a series expansions in the dimensionless spin; in some cases we are able to resum these series into closed-form expressions. Moreover, we observe the existence of intriguing relations between the corrections to the parity-odd multipoles $S_{2n}\neq 0$ and $M_{2n+1}\neq 0$ that break equatorial symmetry, and the parity-preserving corrections that only modify $S_{2n+1}$ and $M_{2n}$. Further, we comment on the higher-derivative corrections to multipole ratios for Kerr, and we discuss the phenomenological implications of the corrections to the multipole moments for current and future gravitational wave experiments.