Relativistic theory of surficial Love numbers

TL;DR

This paper advances the relativistic understanding of surficial Love numbers, providing refined definitions, a unified theory for different bodies, and simplified computational methods, with implications for gravitational physics.

Contribution

It extends and clarifies the relativistic theory of surficial Love numbers, unifies the treatment for material bodies and black holes, and simplifies their computation.

Findings

Refined the definition of surficial Love numbers in terms of surface curvature.

Developed a unified theory applicable to both material bodies and black holes.

Derived a compactness-dependent relation between surficial and gravitational Love numbers.

Abstract

A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar, and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.