Exact Regular Black Hole Solutions with de Sitter Cores and Hagedorn Fluid

TL;DR

This paper presents three exact black hole solutions with de Sitter cores and Hagedorn fluids, exploring their properties, shadows, and dynamic evolution, including potential transitions between regular and singular states.

Contribution

The paper introduces new exact solutions to Einstein's equations for black holes with variable equations of state and Hagedorn fluids, including a dynamic model of gravitational collapse.

Findings

Black hole solutions with de Sitter cores and Hagedorn fluids are derived.

Black hole shadows can constrain model parameters.

Black holes can transition between regular and singular states during evolution.

Abstract

In this paper, we present three exact solutions to the Einstein field equations, each illustrating different black hole models. The first solution introduces a black hole with a variable equation of state, $P = k(r)\rho$, which can represent both singular and regular black holes depending on the parameters $M_0$ and $w_0$. The second solution features a black hole with Hagedorn fluid, relevant to the late stages of black hole formation, and reveals similarities to the first solution by also describing both singular and regular black holes in a specific case. Furthermore, we investigate the shadows cast by these black hole solutions to constrain their parameters. Recognizing that real astrophysical black holes are dynamic, we developed a third, dynamical solution that addresses gravitational collapse and suggests the potential formation of naked singularities. This indicates that a black hole can transition from regular to singular and back to regular during its evolution.