Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour

TL;DR

This paper investigates homothetic scalar field collapse, identifying solutions with dispersal, black holes, and naked singularities, highlighting critical behavior and the role of self-similarity in gravitational collapse.

Contribution

It introduces a new autonomous system approach to analyze scalar field collapse, revealing classes of solutions and critical phenomena with detailed properties.

Findings

Discovered solutions with non-singular origins that disperse

Identified solutions leading to black holes and naked singularities

Explored critical evolution between different collapse outcomes

Abstract

Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again. There is a singularity at one point of these solutions, however it is not visible to observers at finite radius. The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes. The properties of these solutions are discussed in detail. The paper also contains some speculation about the significance of self-similarity in recent numerical studies.