Local and global gravitational aspects of domain wall space-times

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. The assumption of homogeneity, isotropy, and geodesic completenes 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 lineelement 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 a kink-like scalar field configuration. These vacuum domain walls fall in three classes depending on the value of their σ: (1) extreme walls with σ = σext are planar, static walls corresponding to supersymmetric configurations, (2) non-extreme walls with σ = σnon > σext correspond to expanding bubbles with observers on either side of the wall being inside the bubble, and (3) ultra-extreme walls with σ = σ ultra < σext 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.

Bent domain walls as braneworlds

“…Our motivation for this sign choice is that such models can be naturally obtained by compactifying supergravity theories in 10D by using the Freund-Rubin ansatz [16], for example, compactifying the IIB string theory on AdS 5 × S 5 [17]. Other examples of domain walls in supergravity have been considered in [18,19]. A possibility that the world may look like a domain wall in the context of Hořava-Witten theory [7] has been pursued in [20], and possibilities for inflation in this model were studied in [21].…”

Bent Bogomol’nyi-Prasad-Sommerfield domain walls ofD=5,N=2gauged supergravity coupled to hypermultiplets

“…the space-time on the wall is AdS. [The thin AdS vacuum domain walls, with the negative (as well as positive) curvature were first studied in D=4 in [14]. For generalizations to D-dimensions, see, e.g.…”

Domain Wall World(s)

“…(This part of the review is primarily based on a much earlier work on domain walls in four-dimensional N=1 supergravity, initiated in [14], its generalizations to non-BPS solutions were given in [15] and reviewed in [16]; for a recent work on a generalization of the analysis to D-dimensions see [17] and references therein.) (ii) We shall then turn to the discussion of the properties of domain walls in N=2 D=5 gauged supergravity (with vector multiplets), leading to the "no-go" theorem for the implementation of the Randall-Sundrum scenario.…”