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