Self-Similar Collapse of Scalar Field with Plane Symmetry

TL;DR

This paper analytically derives all plane symmetric self-similar solutions in Einstein's gravity, showing some represent scalar field collapse leading to spacelike singularities without black hole formation or trapped surfaces.

Contribution

It provides a complete classification of self-similar solutions in this setting and analyzes their properties, revealing collapse outcomes without horizon formation.

Findings

Solutions are analytically derived in closed form.

Collapse results in spacelike singularities without black holes.

Trapped surfaces are never formed during collapse.

Abstract

Plane symmetric self-similar solutions to Einstein's four-dimensional theory of gravity are studied and all such solutions are given analytically in closed form. The local and global properties of these solutions are investigated and it is shown that some of the solutions can be interpreted as representing gravitational collapse of the scalar field. During the collapse, trapped surfaces are never developed. As a result, no black hole is formed. Although the collapse always ends with spacetime singularities, it is found that these singularities are spacelike and not naked.