Love numbers of black holes and compact objects

Abstract

The Love numbers of a gravitating body are response coefficients encoding its tidal deformability. In compact binary systems, they appear in the gravitational waveform during the inspiral phase and will be measurable by upcoming gravitational-wave observatories. This review provides a comprehensive and pedagogical account of the theoretical foundations of Love numbers and surveys the most recent advances in the study of tidal effects in compact objects, with particular emphasis on black holes and neutron stars. We begin with a gentle introduction to tidal effects in Newtonian gravity, leading into a discussion of how to robustly define tidal responses in general relativity using the effective field theory and post-Newtonian frameworks. After an overview of the perturbation theory of black holes and neutron stars, we review the computation of Love numbers and dissipative response coefficients in a wide range of settings, including the static, dynamical, and nonlinear tidal responses of Kerr black holes and neutron stars in four-dimensional general relativity. We further discuss the extension of these results to charged black holes and a number of "new physics" scenarios, including higher-dimensional black holes and other black objects, (anti-) de Sitter black holes, supergravity black holes, and theories beyond general relativity. Finally we provide an overview of the tantalizing zoo of hidden symmetries of general relativity that have been uncovered in the attempt to explain the famous vanishing of static black hole Love numbers.