Collapse and dispersal in massless scalar field models

TL;DR

This paper establishes a sufficient condition for dispersal in massless scalar field models, showing that a change in the gradient's nature from timelike to spacelike guarantees dispersal, regardless of spacetime symmetry.

Contribution

It provides a novel, symmetry-independent criterion linking gradient change to dispersal in scalar field collapse scenarios.

Findings

Gradient change from timelike to spacelike implies dispersal

The result is demonstrated explicitly with Roberts' scalar field solution

Implications for understanding scalar field collapse and dispersal are discussed

Abstract

The phenomena of collapse and dispersal for a massless scalar field has drawn considerable interest in recent years, mainly from a numerical perspective. We give here a sufficient condition for the dispersal to take place for a scalar field that initially begins with a collapse. It is shown that the change of the gradient of the scalar field from a timelike to a spacelike vector must be necessarily accompanied by the dispersal of the scalar field. This result holds independently of any symmetries of the spacetime. We demonstrate the result explicitly by means of an example, which is the scalar field solution given by Roberts. The implications of the result are discussed.