Year: 2026
Type: preprint
Abstract: Black hole uniqueness is one of the fundamental predictions of general relativity: the spherically symmetric Schwarzschild--Tangherlini spacetime is the unique regular, asymptotically flat, static vacuum black hole solution of Einstein's equations. We show that an analogous result holds perturbatively in Lovelock gravity. Assuming the appropriate positive-mass rigidity statement, any regular, asymptotically flat, static vacuum black hole solution of Lovelock gravity on a generic branch admitting a regular Taylor expansion about general relativity is uniquely determined, at fixed ADM mass, by the corresponding spherically symmetric Lovelock black hole solution. In particular, Einstein--Gauss--Bonnet gravity admits no distinct nonspherical static branch perturbatively connected to Schwarzschild--Tangherlini, and the unique solution is Boulware--Deser. The same recursive mechanism extends to the full Lovelock class. Our result shows that static black hole uniqueness can extend beyond general relativity and is not a property peculiar to the Einstein equations.
Source: arXiv (Cornell University)
Authors: Sharma, Chanchal, Sarkar, Sudipta
Institution: Indian Institute of Technology Gandhinagar
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222986658