Gravitational collapse of spherically-symmetric inhomogeneous dust in the LTB spacetime
Abstract
We study the gravitational collapse of a spherically symmetric, inhomogeneous dust distribution described by the marginally bound Lemaître–Tolman–Bondi (LTB) solution expressed in Painlevé–Gullstrand coordinates. The evolution of the spacetime is fully determined by the Misner–Sharp mass M(t,r) and, consequently, the matter energy density. A Gaussian initial energy density profile was used, parametrized by a central density ρc and width σ. We analyze the evolution of the Misner–Sharp mass, the behavior of radial geodesics of timelike and null observers, and the formation of apparent horizons (AHs). Three distinct regimes of AH formation are identified based on the values of ρc and σ: (1) two pre-existing AHs with the eventual disappearance of the inner horizon, (2) a single AH that splits into two, and (3) a single AH forming at the origin and propagating outward.
