Colliding wave solutions in 2 + 1-dimensions

Abstract

We identified a new metric that describes both colliding electromagnetic shock waves and scalar waves without cosmological constant in 2 + 1-dimensions. To the future of collision point our metric has spacelike singularity so that the electromagnetic solution differs from its 3 + 1-dimensional counterpart. Our interaction region with scalar waves is related through the Kaluza–Klein argument with the 3 + 1-dimensional Schwarzschild spacetime.

Colliding fields in two-dimensional dilaton gravity background

“…Due to the inherent non-linearity involved, which is less stringent in general relativity, finding exact solutions to such problems remain challenging. Newly we have also obtained exact colliding wave solutions of scalar and electromagnetic shock waves in 2+1-dimensions [11].…”