A class of $d$-dimensional regular black holes: Shadows, Thermodynamics and Gravitational collapse

TL;DR

This paper explores a broad class of higher-dimensional regular black holes with de Sitter cores, analyzing their geometric, optical, thermodynamic properties, and gravitational collapse dynamics, extending known models and providing observational constraints.

Contribution

It generalizes regular black hole models to higher dimensions, analyzes their stability, shadows, thermodynamics, and collapse processes, and connects these features with observational data.

Findings

Stable and unstable photon spheres identified.

Shadow size decreases with dimension, charge, and polytropic index.

Regular black holes exhibit phase transitions and entropy deviations.

Abstract

We investigate a general class of $d$-dimensional regular black holes characterized by a de Sitter core, which arises from the gravitational collapse of a polytropic star with an arbitrary polytropic index $n$. This framework generalizes the well-known Bardeen and Hayward black holes to higher dimensions and identifies nonlinear electrodynamics with a magnetic monopole charge as the physical source ensuring spacetime regularity. We analyze the geometric structure and energy conditions, demonstrating that while the Weak and Null Energy Conditions are satisfied, the Strong Energy Condition is violated, a necessary feature for singularity avoidance. Our study of optical properties reveals the existence of stable and unstable photon spheres, with shadows persisting only up to a critical magnetic charge limit; beyond this threshold, the object becomes a horizonless compact object. Numerical results indicate that the shadow size decreases as the dimension $d$, charge $q$, or index $n$ increases, allowing for constraints based on EHT observations of M87* and SgrA*. Thermodynamically, these regular black holes exhibit regions of local stability and phase transitions, with entropy deviating from the standard area law in higher dimensions. Finally, we generalize the Oppenheimer-Snyder-Datt collapse scenario to this background. We track the evolution of horizons, the nature of the trapping horizon, and derive a critical lower bound for the initial stellar radius required for physical black hole formation. Our results show that increasing dimensions and the polytropic index delay the collapse proper time, while magnetic charge facilitates the process by reducing the minimum initial radius. These findings provide new insights into the viability of regular black holes as non-singular endpoints of gravitational collapse in higher-dimensional gravity.