Gravitomagnetic response of an irrotational body to an applied tidal field

TL;DR

This paper recalculates the gravitomagnetic Love numbers for an irrotational body under tidal forces, revealing they are negative, contrasting with positive values in the hydrostatic equilibrium case, using general relativity and post-Newtonian methods.

Contribution

It introduces a more realistic irrotational model for bodies under tidal forces and computes the resulting gravitomagnetic Love numbers, showing they differ significantly from previous hydrostatic assumptions.

Findings

Gravitomagnetic Love numbers are negative in irrotational states.

Love numbers differ dramatically from hydrostatic equilibrium cases.

Results are consistent with full general relativity and post-Newtonian approximations.

Abstract

The deformation of a nonrotating body resulting from the application of a tidal field is measured by two sets of Love numbers associated with the gravitoelectric and gravitomagnetic pieces of the tidal field, respectively. The gravitomagnetic Love numbers were previously computed for fluid bodies, under the assumption that the fluid is in a strict hydrostatic equilibrium that requires the complete absence of internal motions. A more realistic configuration, however, is an irrotational state that establishes, in the course of time, internal motions driven by the gravitomagnetic interaction. We recompute the gravitomagnetic Love numbers for this irrotational state, and show that they are dramatically different from those associated with the strict hydrostatic equilibrium: While the Love numbers are positive in the case of strict hydrostatic equilibrium, they are negative in the irrotational state. Our computations are carried out in the context of perturbation theory in full general relativity, and in a post-Newtonian approximation that reproduces the behavior of the Love numbers when the body's compactness is small.