Tidal deformation of black holes in Lovelock gravity

TL;DR

This work investigates static tidal deformability of black holes in Lovelock gravity, focusing on pure Lovelock and Einstein–Gauss–Bonnet (EGB) theories. The authors develop a perturbative framework separating scalar, tensor, axial, and polar sectors, solve the corresponding master equations for static perturbations, and extract the static tidal Love numbers (TLNs) across spacetime dimensions. They find that pure Lovelock BHs can exhibit vanishing TLNs in specific $(d,N)$ combinations (e.g., certain cases including $d=3N+1$ for tensor and related integer-parameter conditions), while Einstein–Gauss–Bonnet BHs generically have nonzero TLNs, with explicit small-$ ilde{ ext{α}}$ results showing strong coupling dependence. This demonstrates a pronounced sensitivity of BH tidal responses to the underlying gravity theory and dimensionality, offering potential observational avenues to probe higher-curvature corrections via gravitational-wave signatures.

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.