Local and global gravitational aspects of domain wall space-times

TL;DR

This paper analyzes the gravitational effects of different types of vacuum domain walls in space-times with varying cosmological constants, revealing how their energy densities influence global gravitational forces and space-time structures.

Contribution

It classifies vacuum domain walls into three types based on their energy density and explores their global gravitational effects and space-time structures, including supersymmetric and bubble decay configurations.

Findings

Extreme walls are planar and static, corresponding to supersymmetric configurations.

Non-extreme walls are expanding bubbles with repulsive gravitational effects.

Ultra-extreme walls represent false vacuum decay bubbles with attractive gravitational effects.

Abstract

Local and global gravitational effects induced by eternal vacuum domain walls are studied. We concentrate on thin walls between non-equal and non-positive cosmological constants on each side of the wall. These vacuum domain walls fall in three classes depending on the value of their energy density $\sigma$: (1)\ extreme walls with $\sigma = \sigma_{{\text{ext}}}$ are planar, static walls corresponding to supersymmetric configurations, (2)\ non-extreme walls with $\sigma = \sigma_{{\text{non}}} > \sigma_{{\text{ext}}}$ correspond to expanding bubbles with observers on either side of the wall being {\em inside\/} the bubble, and (3)\ ultra-extreme walls with $\sigma = \sigma_{{\text{ultra}}} < \sigma_{{\text{ext}}}$ represent the bubbles of false vacuum decay. On the sides with less negative cosmological constant, the extreme, non-extreme, and ultra-extreme walls exhibit no, repulsive, and attractive effective ``gravitational forces,'' respectively. These ``gravitational forces'' are global effects not caused by local curvature. Since the non-extreme wall encloses observers on both sides, the supersymmetric system has the lowest gravitational mass accessable to outside observers. It is conjectured that similar positive mass protection occurs in all physical systems and that no finite negative mass object can exist inside the universe. We also discuss the global space-time structure of these singularity free space-times and point out intriguing analogies with the causal structure of black holes.