Comment on the Roberts solution for the spherically-symmetric Einstein-scalar field equations

TL;DR

This paper critically examines the Roberts solution for spherically symmetric Einstein-scalar field equations, clarifies its valid cases, and explores its generalizations and relations to other solutions.

Contribution

It corrects the understanding of the Roberts solution's validity and introduces its generalizations and connections to other known solutions.

Findings

Roberts solution only solves the equations in one non-trivial case

Generalization of the Roberts solution is proposed

Relations with other exact solutions are discussed

Abstract

We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.