Brane Waves

TL;DR

This paper investigates five-dimensional algebraically special gravitational waves in brane-world cosmology, showing how bulk plane waves relate to brane dynamics and providing exact solutions illustrating these phenomena.

Contribution

It systematically analyzes algebraically special 5D gravitational waves and their effects on the brane, including explicit solutions and embedding into Siklos spacetimes.

Findings

Bulk gravitational waves can be approximated by plane waves in certain regimes.

The projected non-local stress tensor on the brane resembles a null fluid.

Any plane wave brane can be embedded into a 5D Siklos spacetime.

Abstract

In brane-world cosmology gravitational waves can propagate in the higher dimensions (i.e., in the `bulk'). In some appropriate regimes the bulk gravitational waves may be approximated by plane waves. We systematically study five-dimensional gravitational waves that are algebraically special and of type N. In the most physically relevant case the projected non-local stress tensor on the brane is formally equivalent to the energy-momentum tensor of a null fluid. Some exact solutions are studied to illustrate the features of these branes; in particular, we show explicity that any plane wave brane can be embedded into a 5-dimensional Siklos spacetime. More importantly, it is possible that in some appropriate regime the bulk can be approximated by gravitational plane waves and thus may act as initial conditions for the gravitational field in the bulk (thereby enabling the field equations to be integrated on the brane).