The Tolman-Bondi--Vaidya Spacetime: matching timelike dust to null dust

Abstract

The Tolman-Bondi and Vaidya solutions are two solutions to Einstein equations which describe dust particles and null fluid, respectively. We show that it is possible to match the two solutions in one single spacetime, the Tolman-Bondi--Vaidya spacetime. The new spacetime is divided by a null surface with Tolman-Bondi dust on one side and Vaidya fluid on the other side. The differentiability of the spacetime is discussed. By constructing a specific solution, we show that the metric across the null surface can be at least $C^1$ and the stress-energy tensor is continuous.

5 pages, no figure

References in corpus (1)

• On The Vaidya Limit of the Tolman Model

Cited by in corpus (6)

• Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
• Spherically Symmetric Gravitational Collapse of General Fluids
• Radiative gravitational collapse to spherical, toroidal and higher genus black holes
• T-spheres as a limit of Lemaitre-Tolman-Bondi solutions
• Wave equations on the linear mass Vaidya metric
• On matching LTB and Vaidya spacetimes through a null hypersurface