Vacuum domain walls in D dimensions: Local and global space-time structure

We study local and global gravitational effects of $\left(D-2\right)$-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 a $\left(D-1\right)$-dimensional Freedman-Lemaître-Robertson-Walker universe (with $k=-1,0,1)$ which has a (local) description as either anti–de Sitter, Minkowski or de Sitter 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 (supersymmetric) 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 $D=5.\mathrm{}$