Collision of shock waves in Einstein-Maxwell theory with a cosmological constant: A special solution

Abstract

Postcollision space-times of the Cartesian product form ${M}^{\ensuremath{'}}\ifmmode\times\else\texttimes\fi{}{M}^{\ensuremath{'}\ensuremath{'}}$, where ${M}^{\ensuremath{'}}$ and ${M}^{\ensuremath{'}\ensuremath{'}}$ are two-dimensional manifolds, are known with ${M}^{\ensuremath{'}}$ and ${M}^{\ensuremath{'}\ensuremath{'}}$ having constant curvatures of equal and opposite sign (for the collision of electromagnetic shock waves) or of the same sign (for the collision of gravitational shock waves). We construct here a new explicit postcollision solution of the Einstein-Maxwell vacuum field equations with a cosmological constant for which ${M}^{\ensuremath{'}}$ has constant (nonzero) curvature and ${M}^{\ensuremath{'}\ensuremath{'}}$ has zero curvature.