Tidal deformation of black holes in Lovelock gravity

TL;DR

This paper investigates how black holes in Lovelock gravity respond to external tidal fields, revealing that static tidal Love numbers can vanish or remain non-zero depending on the gravity theory and dimensions, extending known results.

Contribution

It demonstrates that in certain higher-dimensional Lovelock gravity theories, black holes can have zero static tidal Love numbers, generalizing four-dimensional results.

Findings

Pure Lovelock gravity can yield zero static TLNs for black holes.

Einstein-Gauss-Bonnet black holes generally have non-zero static TLNs.

Exceptions occur in specific cases related to axial perturbations.

Abstract

It is well established that black holes in four-dimensional, vacuum, general relativity exhibit vanishing static tidal Love numbers, indicating no multipolar response to the external tidal fields in the static limit. This intriguing feature does not extend to higher-dimensional spacetimes within general relativity, where static black holes can possess non-zero static tidal Love numbers (TLNs). In this work, we have examined the tidal deformation of black holes in Lovelock gravity. We find that, in certain cases within pure Lovelock gravity, the static TLN vanishes, extending the four-dimensional result to specific higher-dimensional settings. On the other hand, black holes in Einstein-Gauss-Bonnet gravity consistently exhibit non-zero static TLNs, with their magnitude depending on the Gauss-Bonnet coupling constant. Exceptions occur only in certain special cases associated with axial perturbations. These results highlight the sensitivity of the multipolar response of a black hole under tidal field, to the underlying theory of gravity and the spacetime dimensions.