Dynamics of Anti-de Sitter Domain Walls

TL;DR

The work addresses the dynamics of Anti-de Sitter domain walls in a five-dimensional Randall-Sundrum–type setting, where the bulk is composed of AdS$_5$ patches possibly containing black hole parameters. By applying the Israel junction conditions to a moving wall with Robertson–Walker symmetries, the authors derive the wall's equation of motion and classify wall trajectories, including both exponential and power-law expansion, as well as bounded and unbounded motions. They investigate the four-dimensional gravity on the wall, showing that a normalizable zero-mode graviton can persist for small bulk horizons, butLorentz-violating effects emerge when a horizon is present, diminishing as the wall expands. Inclusion of matter on the wall yields FRW-like cosmologies with parameter-dependent shifts to the effective radiation content, while a string theory embedding via D3-brane shells proves untenable due to insufficient brane tension. Overall, the paper links domain-wall dynamics to cosmology within brane-world scenarios and discusses the prospects and limitations for recovering four-dimensional gravity in such setups.

Abstract

We study solutions corresponding to moving domain walls in the Randall-Sundrum universe. The bulk geometry is given by patching together black hole solutions in AdS$_5$, and the motion of the wall is determined from the junction equations. Observers on the wall interpret the motion as cosmological expansion or contraction. We describe the possible wall trajectories, and examine the consequences for localized gravity on the wall.