On the structure of black hole interior in a model of scalar quasi-particles within the GR framework

Abstract

We propose an effective, singularity-free model of the black hole interior described entirely by a scalar field with a non-linear self-interaction potential. The interior consists of three layers -- a core, a transition layer, and a crust -- each fixed by the local quasi-particle density and the corresponding extremum of the potential of the field. The crust is a layer of massive, positive-energy thermal excitations above the zero-potential well, beneath a genuine Schwarzschild horizon at $r = 2GM_{\rm ADM}$. The core is an AdS-type region of negative energy density, it simulates a condensate of quasi-particles which carry zero classical kinetic energy and form a negative potential well governed by a negative inverse temperature parameter. The two regions are joined through Israel matching across the transition layer, which sits at an approximately null-gravity hypersurface of maximal regular matter density and where both the sign of the energy density and the type of thermal excitations change. Solving the static Einstein equations, we obtain the metric and mass functions of each layer, the edge equation of state of the crust, the linear stability condition of the null-gravity surface for ordinary and effectively negative mass matter, and the two-temperature thermodynamics linking the kinetic excitations to the negative temperature ground state. The framework unifies core and crust within a single field description and highlights the role of the negative energy AdS core and the associated negative temperature notion in describing black hole interior. In this picture the formation and Hawking evaporation of a black hole appear as a quasi-static cycle of an almost adiabatic thermodynamic engine, with the negative energy core as the working substance.