Fatimah Shojai

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 curvature 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 curvature 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, unlike the unstable Schwarzschild-Tangherlini solution, 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 curvature-regular black holes as possible curvature-singularity-free endpoints of gravitational collapse in higher-dimensional gravity.

Gravitational Landscapes: black holes with linear equations of state in asymptotically safe gravityWe study black holes with a linear equation of state within the framework of asymptotically safe gravity. This study extends previous work on gravitational collapse in asymptotically safe gravity (that has been done for a dust fluid) by taking into account the pressure of stellar matter. We derive modified field equations containing the running gravitational coupling and the cosmological constant as functions of the energy density. The interior space-time of the collapsing star is modeled by the Friedmann-Lemaître-Robertson-Walker metric, while the exterior is described by a static spherically symmetric space-time. Different equations of state from ordinary matter to exotic phantom energy are considered to investigate their impact on black hole structure and horizon formation. Our results illustrate that asymptotically safe gravity can introduce non-singular black hole solutions under specific conditions. These results provide new insights into black hole physics and the avoidance of singularities within the asymptotically safe gravity framework.

We establish an exact bidirectional map between the effective homogeneous interior density of a collapsing star and the exterior metric function in generalized Oppenheimer-Snyder collapse. The Darmois-Israel junction conditions reduce this relation to a purely algebraic form, providing a direct way to reconstruct candidate static geometries and their surface dynamics without solving the corresponding differential field equations separately. Correction powers diagnose models; integer exponents signal ultraviolet completions, while fractional powers identify phenomenological ones. Our framework not only simplifies the construction of regular black holes but also provides a universal benchmark for testing singularity resolution and cosmic censorship in quantum gravity phenomenology.

This paper investigates the existence of cosmological black holes by analyzing the properties of trapping horizons in detail, based on Hayward’s formalism of future outer and past inner trapping horizons, in several dynamical spacetimes embedded in an expanding universe. Through a detailed examination of the McVittie, Culetu, and Sultana–Dyer metrics, as well as the generalized Glass–Mashhoon solution, we evaluate the existence and characteristics of trapping horizons and energy conditions. The Glass–Mashhoon solution provides an analytical model for spherical stellar collapse. However, it is shown that, as long as certain conditions are satisfied, it lacks suitable future outer trapping horizons, meaning it does not represent a cosmological black hole. As a result, the McVittie class of solutions also fails to describe a cosmological black hole. Conversely, the Culetu and Sultana–Dyer spacetimes can describe a cosmological black hole in the matter-dominated early universe, provided that the relevant energy conditions are satisfied.

We consider the third law of thermodynamics for families of 4- and n-dimensional Vaidya black holes, including many of interest. Since there are several versions of the definition of surface gravity as well as the extremality condition for dynamical black holes, we first show that for the considered 4- and n-dimensional Vaidya families, these definitions are consistent with each other. We assume, first, that a non-extremal black hole evolves to an extremality state after a finite time and second, that the weak energy condition for the source holds at all times. We then compare the results of these assumptions and investigate whether there are ranges of black hole parameters where these two assumptions are in conflict.

We consider the third law of thermodynamics for families of 4- and n-dimensional Vaidya black holes, including many of interest. Since there are several versions of the definition of surface gravity as well as the extremality condition for dynamical black holes, we first show that for the considered 4- and n-dimensional Vaidya families, these definitions are consistent with each other. We assume, first, that a non-extremal black hole evolves to an extremality state after a finite time and second, that the weak energy condition for the source holds at all times. We then compare the results of these assumptions and investigate whether there are ranges of black hole parameters where these two assumptions are in conflict.