The Roberts-(A)dS spacetime

TL;DR

This paper explores the structure of Roberts-(A)dS spacetimes, revealing their properties, horizons, and collapse behavior, including higher-dimensional generalizations, within the context of general relativity with a scalar field.

Contribution

It provides a detailed analysis of the global structure and topological aspects of Roberts-(A)dS solutions, including their connection to AdS spacetime and higher-dimensional extensions.

Findings

Spacetime contains a black-hole event horizon depending on parameters.

Spacetime can be attached to exact AdS spacetime on a null hypersurface.

Higher-dimensional Roberts-(A)dS solutions with flat base manifold are constructed.

Abstract

Global structure of the (anti-)de~Sitter ((A)dS) generalization of the Roberts solution in general relativity with a massless scalar field and its topological generalization is clarified. In the case with a negative cosmological constant, the spacetime is asymptotically locally AdS and it contains a black-hole event horizon depending on the parameters. The spacetime may be attached to the exact AdS spacetime in a regular manner on a null hypersurface and the resulting spacetime represents gravitational collapse from a regular initial datum. The higher-dimensional counterpart of this Roberts-(A)dS solution with flat base manifold is also given.