D=3: Singularities in Gravitational Scattering of Scalar Waves

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.