Full spectrum of Love numbers of Reissner-Nordstrom black hole in D-dimensions

TL;DR

This work generalizes tidal Love-number analysis to $D$-dimensional Reissner–Nordström black holes by perturbing the Einstein–Maxwell system and reducing to a $1+1$-dimensional effective theory. The authors derive master equations for tensor, vector, and scalar perturbations, diagonalize the graviton–photon system, and extract Love numbers from the large-distance behavior of static solutions. They confirm vanishing Love numbers for $D=4$, reproduce tensor and vector results in higher dimensions, and reveal a distinctive scalar-sector pattern: vanishing for integer $ ilde{oldell}=rac{oldell}{D-3}$ and logarithmic running for half-integer values, with finite, numerically accessible values otherwise. These results reinforce rigidity/no-hair expectations in four dimensions and provide a comprehensive framework for charged black-hole tidal responses in higher-dimensional Einstein–Maxwell theory, with potential extensions to dyons and nonlinear tidal responses.

Abstract

We present a comprehensive analysis of the full spectrum of tidal Love numbers for Reissner-Nordström (RN) black holes in general spacetime dimensions. By perturbing the Einstein-Maxwell theory around the $D$-dimensional RN background, we derive an effective two dimensional quadratic action encompassing tensor, vector, and scalar-type perturbation sectors. Through diagonalization, we obtain master equations governing each sector and extract the corresponding Love numbers from the asymptotic behavior of the solutions. Our results confirm that all Love numbers vanish for four-dimensional RN black holes. In higher dimensions, the tensor and vector Love numbers reproduce previously known results. For the previously unknown scalar-type Love numbers, we show also they vanish for integer valued effective multipolar indices and display logarithmic running behavior when the corresponding indices are half integers.