Spherically symmetric static solution for colliding null dust

TL;DR

This paper derives a static, spherically symmetric solution to Einstein's equations with colliding null dust streams, exploring its properties, coordinate representations, and connections to dilaton gravity, with matching conditions to known solutions.

Contribution

It presents a novel static solution for colliding null dust under spherical symmetry, including coordinate forms and matching conditions, linking to two-dimensional dilaton gravity.

Findings

Solution in double null and radiation coordinates.

Interior matching with static fluid, exterior with Vaidya solution.

Connection established with two-dimensional dilaton gravity.

Abstract

The Einstein equations are integrated in the presence of two (incoming and outgoing) streams of null dust, under the assumptions of spherical symmetry and staticity. The solution is also written in double null and radiation coordinates and it is reinterpreted as an anisotropic fluid. Interior matching with a static fluid and exterior matching with the Vaidya solution along null hypersurfaces is discussed. The connection with two-dimensional dilaton gravity is established.