Tidal deformability of ultracompact Schwarzschild stars and their approach to the black hole limit

TL;DR

This paper investigates the tidal deformability of ultracompact Schwarzschild stars, showing that their Love numbers decrease exponentially as they approach black hole compactness, contrasting with the logarithmic behavior suggested for other exotic objects.

Contribution

It demonstrates that ultracompact Schwarzschild stars exhibit an exponential decay in Love numbers near the black hole limit, challenging previous conjectures about ECOs.

Findings

Love numbers approach zero as compactness nears the black hole limit

The decay of Love numbers is exponential, not logarithmic

Schwarzschild stars mimic black holes more closely at high compactness

Abstract

A well-known result in general relativity is that the tidal Love numbers of black holes vanish. In contrast, different configurations to a black hole may have non-vanishing Love numbers. For instance, it has been conjectured recently that the Love number of generic exotic compact objects (ECOs) shows a logarithmic behavior. Here we analyze the ultracompact Schwarzschild star which allows the compactness to cross and go beyond the Buchdahl limit. This Schwarzschild star has been shown to be a good black hole mimicker, moreover, it has been found that the Love number of these objects approaches zero as their compactness approaches the black hole limit. Here we complement those results, by showing that the Love number for these configurations follows an exponentially decaying behavior rather than the logarithmic behavior proposed for generic ECOs.