Square Peg in a Circular Hole: Choosing the Right Ansatz for Isolated Black Holes in Generic Gravitational Theories

Yiqi Xie, Jun Zhang, Hector O. Silva, Claudia de Rham, Helvi Witek, and Nicolás Yunes

Phys. Rev. Lett. 126, 241104 – Published 17 June 2021

Abstract

The metric of a spacetime can be greatly simplified if the spacetime is circular. We prove that in generic effective theories of gravity, the spacetime of a stationary, axisymmetric, and asymptotically flat solution must be circular if the solution can be obtained perturbatively from a solution in the general relativity limit. This result applies to a broad class of gravitational theories that include arbitrary scalars and vectors in their light sector, so long as their nonstandard kinetic terms and nonmininal couplings to gravity are treated perturbatively.

Received 5 March 2021
Accepted 3 May 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.241104

Physics Subject Headings (PhySH)

Alternative gravity theories Astrophysical studies of gravity Gravitation

Astronomical black holes Classical black holes

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Yiqi Xie ^1,*, Jun Zhang ^2,1,†, Hector O. Silva ^3,1,‡, Claudia de Rham ^2,4,§, Helvi Witek ^1,∥, and Nicolás Yunes ^1,¶

¹Illinois Center for Advanced Studies of the Universe and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²Theoretical Physics, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom
³Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, D-14476 Potsdam, Germany
⁴CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA