Colliding Spherically Symmetric Null Dust in Equilibrium

Null dust is a model for the incoherent superposition of waves with random polarizations and phases, moving in a single direction with the speed of light. It also describes the high frequency (geometrical optics) approximation for any type (including gravitational) radiation. Null dust is characterized by the energy-momentum tensor T ab = ρll. Neither the energy density ρ nor the null vector l are uniquely determined and the former can be absorbed in the latter by an appropriate rescaling. Various exact solutions of the Einstein equations in the presence of null dust are known , but certainly the most famous of them is Vaidya’s shining star solution . The energy-momentum tensor describing the collision of two streams of null dust (with propagation vectors k and l pointing in opposite spatial directions) is a sum of the two single null dust energy-momentum terms: