Brane worlds: the gravity of escaping matter

TL;DR

This paper explores how matter escaping from a brane in a five-dimensional model generates spherical gravitational waves that propagate causally, affecting the four-dimensional spacetime without violating Einstein's equations.

Contribution

It introduces a linearized analysis of matter escape in brane worlds, showing the resulting gravitational effects are spherical waves that leave the brane causally and do not violate Einstein's equations.

Findings

Matter escape produces spherical gravitational waves.

The induced metric does not satisfy four-dimensional Einstein equations.

Gravitational effects disappear causally behind the wave.

Abstract

In the framework of a five-dimensional model with one 3-brane and an infinite extra dimension, we discuss a process in which matter escapes from the brane and propagates into the bulk to arbitrarily large distances. An example is a decay of a particle of mass $2m$ residing on the brane into two particles of mass $m$ that leave the brane and accelerate away. We calculate, in the linearized theory, the metric induced by these particles on the brane. This metric does not obey the four-dimensional Einstein equations and corresponds to a spherical gravity wave propagating along the four-dimensional future light cone. The four-dimensional space-time left behind the spherical wave is flat, so the gravitational field induced in the brane world by matter escaping from the brane disappears in a causal way.