A Potential Black Hole Mimicker From Non-Minimal Coupling

Abstract

We present a class of horizonless, regular ultra-compact objects arising in a theory of gravity that allows curvature-fluid coupling. The non-minimal interaction between fluid variables and the Ricci scalar generates a vacuum-like equation of state in the interior, while the exterior remains exactly Schwarzschild. The two spacetimes are glued through a thin shell at the junction. The interior metric is non-singular, the shell acquires a stiff-matter equation of state, and near-horizon compactness allows the configuration to mimic black-hole phenomenology without an event horizon. For radii in the astrophysically motivated range $5$--$7$ km, imposed as an external input rather than predicted by the theory, the model's mass-compactness relation maps this radius window onto a mass window of $1.4$-$2.1M_{\odot }$ for a suitable choice of the curvature-fluid coupling coefficient. We carry out a detailed stability analysis of the shell in the frozen-bulk approximation, identify the compactness window in which the interior is everywhere regular and the shell is stable, and quantify the accuracy of the frozen-bulk approximation through an explicit adiabaticity parameter. We then develop the surface thermodynamics of the shell assuming a first order phase transition-like origin of the ultra-compact object. This idea then gives rise to shell temperature and radiation, the shell temperature scaling $T_{\Sigma }\propto M^{-1/2}$ turns out to be a falsifiable predictions of the model.

arXiv commentA corrected and enlarged version. Contains 22 pages and 3 figures