Gravitational collapse in general relativity and its extensions

Abstract

General Relativity predicts the formation of singularities in black holes. These singularities signal a breakdown of the theory and suggest the need for a new approach that resolves this issue. In this work, we explore modifications of General Relativity through infinite higher-order curvature corrections, leading to regular black holes. We review the dynamics of gravitational collapse using the thin-shell formalism in D-dimensional spacetimes, focusing on both the Schwarzschild and regular Hayward black holes. Two matter models are considered: pressureless dust and matter subject to a pressure p = ωσ. Through analytical and numerical analysis, we characterize the effective potential governing the shell evolution and identify conditions under which gravitational collapse is halted. We show that, in contrast to the singular Schwarzschild case, the collapse of the shell does not give rise to a singularity when using the Hayward metric and even presents an inaccessible region near R = 0 under pressure. These results contribute to the understanding of regular black hole formation dynamics and highlight the relevance of higher-order gravitational corrections in resolving singularities.