Quasi-local masses and cosmological coupling of black holes and mimickers

TL;DR

This paper investigates how the masses of compact objects like black holes may be influenced by cosmological dynamics, revealing that such coupling depends on the mass definition used, with implications for understanding black hole nature.

Contribution

It clarifies the conditions under which cosmological coupling occurs, linking it to the choice of quasi-local versus nonlocal mass definitions, and distinguishes between singular and nonsingular objects.

Findings

Black holes embedded in cosmological backgrounds do not exhibit coupling when using the MS mass.

Nonsingular compact objects show cosmological coupling via their MS mass.

Observational evidence of coupling could indicate nonsingular black hole nature.

Abstract

Motivated by the recent heated debate on whether the masses of local objects, such as compact stars or black holes (BHs), may be affected by the large-scale, cosmological dynamics, we analyze the conditions under which, in a general relativity framework, such a coupling small/large scales is allowed. We shed light on some controversial arguments, which have been used to rule out the latter possibility. We find that the cosmological coupling occurs whenever the energy of the central objects is quantified by the quasi-local Misner-Sharp mass (MS). Conversely, the decoupling occurs whenever the MS mass is fully equivalent to the (nonlocal) Arnowitt-Deser-Misner (ADM) mass. Consequently, for singular BHs embedded in cosmological backgrounds, like the Schwarzschild-de Sitter or McVittie solutions, we show that there is no cosmological coupling, confirming previous results in the literature. Furthermore, we show that nonsingular compact objects couple to the cosmological background, as quantified by their MS mass. We conclude that observational evidence of cosmological coupling of astrophysical BHs would be the smoking gun of their nonsingular nature.