Tidal Love numbers of Proca stars

TL;DR

This paper calculates the tidal Love numbers of Proca stars, revealing their similarities to scalar boson stars and providing insights into their potential as exotic compact objects and dark matter candidates.

Contribution

It introduces the first detailed computation of electric and magnetic tidal Love numbers for spherically symmetric Proca stars, expanding understanding of their gravitational properties.

Findings

Proca stars have positive electric and negative magnetic quadrupolar Love numbers.

Their Love numbers are closer in magnitude compared to scalar boson stars at the same compactness.

Electric Love numbers are slightly larger in magnitude than magnetic ones for Proca stars.

Abstract

Proca stars (arXiv:1508.05395) are everywhere regular, asymptotically flat self-gravitating solitons composed of complex, massive vector bosons, forming a macroscopic, star-sized, Bose-Einstein condensate. They have been suggested as a classical, dynamical model of exotic compact objects, black hole mimickers and dark matter candidates. In spherical symmetry, they are qualitatively similar to their scalar cousins, the standard (scalar) boson stars in all respects studied so far. Here we study the tidal deformability and the quadrupolar tidal Love numbers, both electric-type and magnetic-type, of spherically symmetric Proca stars. The equations for the perturbations are derived and the numerical values of the Love numbers for some concrete background solutions are computed. We observe that both Love numbers are qualitatively similar to the ones of the scalar boson stars; in particular, the electric-type (magnetic-type) quadrupolar Love numbers are positive (negative) for Proca stars. Quantitatively, for the same compactness, the electric and magnetic Love numbers in the Proca case are closer (in magnitude) than in the scalar case, with the electric Love numbers having a slightly larger magnitude than the magnetic ones.