Local and global gravitational aspects of domain wall space-times

Local and global gravitational effects induced by eternal vacuum domain walls are studied. We concentrate on thin walls between nonequal and nonpositive cosmological constants on each side of the wall. The assumption of homogeneity, isotropy, and geodesic completeness of the space-time intrinsic to the wall as described in the comoving coordinate system and the constraint that the same symmetries hold in hypersurfaces parallel to the wall yield a general Ansatz for the line element of space-time. We restrict the problem further by demanding that the wall’s surface energy density, σ, is positive and by requiring that the infinitely thin wall represents a thin-wall limit of kinklike scalar field configuration. These vacuum domain walls fall in three classes depending on the value of their σ: (1) extreme walls with σ=${\mathrm{\sigma }}_{\mathrm{ext}}$ are planar, static walls corresponding to supersymmetric configurations, (2) nonextreme walls with σ=${\mathrm{\sigma }}_{\mathrm{non}}$>${\mathrm{\sigma }}_{\mathrm{ext}}$ correspond to expanding bubbles with observers on either side of the wall being inside the bubble, and (3) ultraextreme walls with σ=${\mathrm{\sigma }}_{\mathrm{ultra}}$<${\mathrm{\sigma }}_{\mathrm{ext}}$ represent the bubbles of false vacuum decay. On the sides with less negative cosmological constant, the extreme, nonextreme, and ultraextreme walls exhibit no, repulsive, and attractive effective ‘‘gravitational forces,’’ respectively. These ‘‘gravitational forces’’ are global effects not caused by local curvature. Since the nonextreme wall encloses observers on both sides, the supersymmetric system has the lowest gravitational mass accessible 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.