Relativistic theory of tidal Love numbers

TL;DR

This paper develops a relativistic framework for tidal Love numbers, applicable to compact objects like neutron stars and black holes, providing new insights into their internal structure and gravitational wave signatures.

Contribution

It extends previous Newtonian models to relativistic regimes, defining and calculating electric and magnetic Love numbers for various compact bodies, including black holes.

Findings

Relativistic Love numbers for neutron stars depend on internal structure.

Black holes have zero relativistic Love numbers.

The theory enables better interpretation of gravitational-wave data.

Abstract

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.