D=3: Singularities in Gravitational Scattering of Scalar Waves

TL;DR

This paper constructs exact three-dimensional Einstein-scalar spacetimes from four-dimensional vacua, analyzing their singularities and showing that regular incoming waves inevitably lead to future singularities, unlike in four dimensions.

Contribution

It provides a new class of exact D=3 Einstein-scalar solutions derived from D=4 vacua and investigates the conditions for regularity and singularity formation.

Findings

Singularities are generically present in the D=3 solutions.

Regular incoming waves do not prevent future singularities in D=3.

The scalar curvature singularities are not necessarily caused by incoming wave singularities.

Abstract

Family of exact spacetimes of D=3 Einstein gravity interacting with massless scalar field is obtained by suitable dimensional reduction of a class of D=4 plane-symmetric Einstein vacua. These D=3 spacetimes describe collisions of line-fronted asymptotically null excitations and are generically singular to the future. The solution for the scalar field can be decomposed into the Fourier-Bessel modes around the background solitons. The criteria of regularity of incoming waves are found. It is shown that the appearance of the scalar curvature singularities need not stem from singularities of incoming waves. Moreover, in distinction to D=4 case, for all solutions with regular incoming waves the final singularities are inevitable.