Tidal Love Numbers of Black Holes

 In this talk, I will first discuss the tidal response of rotating BTZ black holes to scalar perturbations. I will show that the real part of the response function is non-zero, leading to finite tidal Love numbers (TLNs). The response also exhibits scale-dependent logarithmic running. I will further discuss the qualitatively similar behaviour of extremal rotating BTZ black holes and outline a procedure for computing the tidal response of charged rotating BTZ spacetimes. Motivated by the vanishing of static TLNs for four-dimensional vacuum black holes in general relativity, I will then explore tidal deformation in higher-curvature theories of gravity. In pure Lovelock gravity, static TLNs vanish in certain cases, extending the four-dimensional result to specific higher-dimensional scenarios. In contrast, black holes in Einstein–Gauss–Bonnet gravity generally possess non-zero TLNs, whose magnitude depends on the Gauss–Bonnet coupling. These results highlight the strong dependence of black-hole tidal response on both spacetime dimensionality and the underlying theory of gravity.