Vacuum Domain Walls in D-dimensions: Local and Global Space-Time Structure

TL;DR

This paper analyzes the gravitational effects of vacuum domain walls in D-dimensional space-time, classifying their local and global structures based on tension and cosmological constants, with implications for higher-dimensional theories.

Contribution

It provides a systematic classification of vacuum domain walls' space-time structures in arbitrary dimensions, including their local and global geometries and phenomenological implications.

Findings

Universal local and global space-time structures for domain walls in any dimension.

Classification based on tension and cosmological constants, including anti-de Sitter, Minkowski, and deSitter geometries.

Specific insights into 5-dimensional domain walls and their phenomenological relevance.

Abstract

We study local and global gravitational effects of (D-2)-brane configurations (domain-walls) in the vacuum of D-dimensional space-time. We focus on infinitely thin vacuum domain walls with arbitrary cosmological constants on either side of the wall. In the comoving frame of the wall we derive a general metric Ansatz, consistent with the homogeneity and isotropy of the space-time intrinsic to the wall, and employ Israel's matching conditions at the wall. The space-time, intrinsic to the wall, is that of (D-1)-dimensional Freedman-Lemaitre-Robertson-Walker universe (with k=-1,0,1) which has a (local) description as either anti-deSitter, Minkowski or deSitter space-time. For each of these geometries, we provide a systematic classification of the local and global space-time structure transverse to the walls, for those with both positive and negative tension; they fall into different classes according to the values of their energy density relative to that of the extreme (superysmmetric) configurations. We find that in any dimension D, both local and global space-time structure for each class of domain-walls is universal. We also comment on the phenomenological implications of these walls in the special case of D=5.