Exact gravitational plane waves and two-dimensional gravity

TL;DR

This paper analyzes exact solutions of gravitational plane waves coupled with scalar fields, revealing their interactions, singularities, and regular solutions, and explores their interpretation as a two-dimensional gravity model with potential singularity resolution.

Contribution

It presents a comprehensive set of exact solutions for colliding gravitational and scalar waves, and links four-dimensional Einstein theory to an exactly solvable two-dimensional gravity model.

Findings

Existence of colliding wave solutions with scalar fields

Identification of singular and regular spacetime configurations

Proposal of a mechanism to remove singularities via short-distance corrections

Abstract

We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves and, for generic initial data, produce a spacetime singularity at the focusing hypersurface. There is, in addition, an infinite family of regular solutions and an intriguing static geometry supported by scalar fields. Upon dimensional reduction, the theory can be viewed as an exactly solvable two-dimensional gravity model. This provides a new viewpoint on the gravitational dynamics. Finally, we comment on a simple mechanism by which short-distance corrections in the two-dimensional model can remove the singularity.