We study here the unhindered gravitational collapse of spatially homogeneous (SH) scalar fields with a potential , as well as vector fields with a potential where and is the metric tensor. We show that in both cases, classes of potentials exist that give rise to black holes or naked singularities. The strength of the naked singularity when it occurs is examined, and these are found to be gravitationally strong in the sense of Tipler, for a wide class of respective potentials (for both scalar and vector fields). We match the collapsing scalar or vector field with a generalized Vaidya spacetime outside. We highlight that full generality is maintained within the domain of SH scalar or vector field collapse.
We study the model of spherically symmetric and spatially homogeneous gravitational collapse of a minimally coupled scalar field. Our study focuses on obtaining the scalar field potential that leads to a final equilibrium state in the gravitational collapse. We demonstrate the existence of a class of scalar field solutions that can indeed result in such an end equilibrium state.
In this paper, working in a geometrical, frame-independent and ansatz-independent formalism, we analytically investigate the gravitational collapse a mass-less scalar field in a spherically symmetric space-time. This is one of the fundamental matter fields determined by the Lagrangian formulation. We identify a single dimensionless parameter, that determines the end-state to be a black-hole or complete dispersal and a locally naked null singularity, which exists as a critical case between the previous two end-states. The governing parameter, being dimensionless, makes the result scale independent, thus confirming the universality and criticality that was observed in extensive numerical studies by various authors.
In this paper, we observe the collapse of a mass-less scalar field covariantly. We show that the strengths of the collapsing and dispersing modes of this scalar field will decide whether the collapse will end up in a black-hole or disperse. We find a locally naked null singularity as a critical case between these two and confirm that there is a single dimensionless parameter that determine the end state. This work is ansatz-independent, hence, true for all mass-less scalar field families. We also show that the geometrical mass of these singularities go to zero.
A major issue in general relativity and blackhole physics today is to determine the conditions when the spacetime singularities forming as end-states of gravitational collapse are visible to external observers, and when these are hidden within the event horizon of a black-hole. We show here that such a causal structure of singularity, in terms of its visibility or otherwise, is determined by the dynamics of the apparent horizon and trapped surfaces forming during collapse of massive matter clouds. It turns out that the relative timing of formation of trapped surfaces and the singularity plays a crucial role here. The dynamics of apparent horizon governs the visibility of singularity, and we characterize precise conditions here for spherically symmetric collapse with a general type-I matter field. This is done in terms of the existence of outgoing null geodesic families from the central singularity. These results hold under generic initial data satisfying $\mathcal{C}^2$ regularity and the weak energy condition.
7 October 2026 in General Relativity and Gravitation