Null deformed domain wall

Abstract

We study null 1/4 BPS deformations of flat Domain Wall solutions (NDDW) in N = 2, d = 5 gauged supergravity with hypermultiplets and vector multiplets coupled. These are uncharged timedependent configurations and contain as special case, 1/2 supersymmetric flat domain walls (DW) and, as well, 1/2 BPS null solutions of the ungauged supergravity. Combining our analysis with the classification method initiated by Gauntlett et al., we prove that all the possible deformations of the DW have origin in the hypermultiplet sector or/and are null. Here, we classify all the null deformations: we show that they naturally organize in "gauging" (v-deformation) and "non gauging" (u-deformation). They have different properties: only in presence of v-deformation the solution is supported by a timedependent scalar potential. Furthermore we show that u-deformation forces the number of multiplets coupled to be different by one. We discuss the general procedure for constructing explicit solutions, stressing the crucial role taken by the integrability conditions of the scalars as spacetime functions. Two analytical solutions are presented. Finally, we comment on the holographic applications of NDDW, in relation with the recently proposed timedependent AdS/CFT.

First-order framework and domain-wall/brane-cosmology correspondence

“…Instead, in this regime one recovers the previous analysis with the scalar potential (20). Thus V 2 0 /σ is assumed to be the coupling connecting asymptotic regimes of the exact potential (18) given in the form…”

“…On the domain walls, the brane is flat assuming a four-dimensional Minkowski geometry [1], whereas far from the domain walls the brane is bent [7,8] and assumes a four-dimensional Anti-de-Sitter (AdS 4 ) geometry -see, e.g., Refs. [11,12,13,14,15,16,17,18,19,20,21,22].…”

Flow equations for non-BPS extremal black holes

“…When the domain-wall is supported by scalar fields (we neglect charged domain-walls like those constructed in [20,21]), and for p = 2, the effective action follows from the lagrangian…”

NEITHER BLACK HOLES NOR REGULAR SOLITONS: A NO-GO THEOREM

“…Nevertheless, the domain walls, together with some of their deformations [22], are the only configurations studied in full generality for all the possible multiplets coupling. This is not true for black holes, which have been considered in full extent only in presence of vector multiplets [23,24,25,10,26,27,28,29,30].…”

“…where the consistency imposes Λ 2 + f r f r = 1. By the use of the identities of the quaternionic manifold, the hyperini equation turns out to be equivalent (see also [12,22]) to…”