Regularity of initial data in dynamical massless scalar field models

TL;DR

This paper investigates the regularity conditions of initial data in spherically symmetric massless scalar field models, identifying models with unavoidable central singularities and implications for gravitational collapse and cosmology.

Contribution

It generalizes known solutions and characterizes models with inherent singularities, informing the selection of initial data for dynamical studies.

Findings

Identifies conditions leading to central singularities in scalar field models.

Classifies models based on regularity of initial data.

Highlights implications for gravitational collapse and cosmological evolution.

Abstract

We discuss here the issue of regularity of initial data for dynamical spherically symmetric massless scalar field models in a spacetime. Generalizing the known solutions of Einstein equations given in this case by Wyman and Roberts, we examine the issue of regularity on a given spacelike surface, especially when the gradient of the field is spacelike. In particular, we isolate the class of models which would have necessarily a singularity at the center, and therefore these would be unsuitable for studying either gravitational collapse or dynamical evolutions in cosmology.