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

TL;DR

This paper calculates the tidal Love numbers for Reissner-Nordström black holes across various dimensions, revealing they vanish in four dimensions and exhibit specific behaviors in higher dimensions, including logarithmic running for certain indices.

Contribution

It provides a comprehensive derivation of all Love numbers for RN black holes in arbitrary dimensions, including new results for scalar-type Love numbers.

Findings

All Love numbers vanish in four-dimensional RN black holes.

Tensor and vector Love numbers in higher dimensions match previous results.

Scalar Love numbers vanish for integer indices and show logarithmic behavior for half-integer indices.

Abstract

We present a comprehensive analysis of the full spectrum of tidal Love numbers for Reissner-Nordstr\"om (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.