Black Hole Multipoles in Higher-Derivative Gravity

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 $S_{2n}\ne 0$ and $M_{2n+1}\ne 0$ 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.

31 pages + Appendix, 13 figures, Mathematica notebook with all expansions used in the paper. Updated to match published version

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• The curvature dependence of gravitational-wave tests of General Relativity
• Exact solution for rotating black holes in parity-violating gravity
• Vacuum Spacetime With Multipole Moments: The Minimal Size Conjecture, Black Hole Shadow, and Gravitational Wave Observables
• Observational features of reflection asymmetric black holes
• Higher-derivative Heterotic Kerr-Sen Black Holes
• Consistent Four-derivative Heterotic Truncations and the Kerr-Sen Solution
• Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
• On Supersymmetric Multipole Ratios
• Quasinormal modes and their excitation beyond general relativity. II: isospectrality loss in gravitational waveforms
• The trace of field equations for higher-derivative gravity and an equality associating the Lagrangian density with a divergence term