Ordinary and Dilatonic Domain Walls: Solutions and Induced Space-Times

TL;DR

This paper classifies and analyzes various types of domain walls in space-time, including their solutions and causal structures, with applications to string theory and black hole analogies.

Contribution

It provides a unified treatment of domain wall configurations, including new solutions involving dilatonic walls relevant to string theory.

Findings

Classified domain walls into extreme, non-extreme, and ultra-extreme types.

Found that space-times with these walls have black hole-like causal structures without singularities.

Identified similarities between dilatonic walls and charged dilatonic black holes.

Abstract

Recent developments in unifying treatment of domain wall configurations and their global space-time structure is presented. Domain walls between vacua of non-equal cosmological constant fall in three classes depending on the value of their energy density $\sigma$: (i) extreme walls with $\sigma=\sigma_{ext}$ are planar, static walls corresponding to the supersymmetric configurations, (ii) non-extreme walls with $\sigma>\sigma_{ext}$ are expanding bubbles with two insides, (iii) ultra-extreme walls with $\sigma<\sigma_{ext}$ are bubbles of false vacuum decay. As a prototype exhibiting all three types of configurations vacuum walls between Minkowski and anti-deSitter vacua are discussed. Space-times associated with these walls exhibit non-trivial causal structure closely related to the one of the corresponding extreme and non-extreme charged black holes, however, without singularities. Recently discovered extreme dilatonic walls, pertinent to string theory, are also addressed. They are static, planar domain walls with metric in the string frame being {\it flat} everywhere. Intriguing similarities between the global space-time of dilatonic walls and that of charged dilatonic black holes are pointed out.