Black hole (BH) junction conditions. Exterior BH geometry with an interior cloud and a new fluid of strings with integrable singularities

TL;DR

The paper addresses central singularities and inner-horizon instabilities in black holes by introducing interior geometries with integrable singularities (IS). It constructs a new fluid of strings (FS) interior and analyzes a cloud of strings (CS) interior as IS sources, both matched to a Reissner–Nordström exterior via Israel–Darmois junction conditions, ensuring temperature continuity at the interface and linking tangential-pressure discontinuities to phase transitions. A key result is a finite conserved energy M achieved through a geometrical screening of the string-cloud density, with the interior IS eliminating the inner horizon and enabling finite tidal effects. The work provides explicit interior–exterior matchings, derives constraints on parameters (e.g., $a$, $l$, $b$, $h$, $Q$), and shows how phase transitions can arise or be suppressed at the horizon, offering a thermodynamic perspective on BH interiors with potential implications for quantum gravity and regularization of central singularities.

Abstract

Regular black holes are often used to address singularities, but they typically involve a potentially unstable de Sitter core and an internal horizon that breaks predictability. Integrable singularities (IS) have recently gained attention because they avoid both issues and exhibit finite tidal forces, allowing nondestructive radial infall. First, we present a new BH solution sourced by a string fluid (FS) that exhibits an IS. Motivated by the divergence of the conserved energy in the cloud of strings (CS) model, we introduce an energy density profile based on the screening of the CS energy density within an FS framework, yielding a finite conserved energy. On the other hand, it has been proposed \cite{Ovalle:2024wtv} that an interior region, rather than a pointlike mass, can generate a Schwarzschild BH exterior region. Secondly, motivated by the variety of BH solutions with singularities in the literature, we establish the conditions that an interior region with an IS must satisfy to represent a generic exterior BH solution, with Schwarzschild being only a particular case of the latter. We derive the junction conditions (JC) between the interior and exterior regions, showing that they lead to temperature continuity at the interface, while discontinuities in tangential pressure lead to phase transitions. We propose that the nature of the interior region is described by CS and FS, while the exterior corresponds to Reissner Nordström.

Figures (2)

• Figure 1: $f(r)_{(fs)}$ for $b=1,M=0.8,0.9,1$. We observe the absence of a potentially unstable inner horizon.
• Figure 2: Schematic representation of the interior region $r \in [0,h]$ and the exterior region extending from $r = h$ to the black hole boundary.