Curvature singularities: The good, the bad, and the naked

Abstract

Necessary conditions are proposed for the admissibility of singular classical solutions with 3 + 1-dimensional Poincare invariance to five-dimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain bounded above for a solution to be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem.e-print archive: http://xxx.lanLgov/hep-th/0002160 680

Non-supersymmetric membrane flows from fake supergravity and multi-trace deformations

“…The second of these equations can be derived by starting from the equation of motion for the independent scalar fields ϕ I , 11) noticing that the last equation in (2.6) implies that 12) and adding a term to ensure that the sum over i is zero, in agreement with the constraint (2.4).…”

“…In fact, the curvature singularity of the supersymmetric metric, for which the Ricci scalar behaves like R 4 ∼ (1 − ρ) −1/2 as ρ → 1, is milder that the curvature singularity of the non-supersymmetric metrics, for which R 4 ∼ (1 − ρ) −3/2 as ρ → 1. Moreover, the singularity is null for the supersymmetric case but timelike for the non-supersymmetric metric [11]. Nevertheless, in both cases the singularity is 'good' according to the criterion of [11] since the scalar potential (4.24) is bounded from above, not only on-shell but even off-shell.…”

“…Moreover, the singularity is null for the supersymmetric case but timelike for the non-supersymmetric metric [11]. Nevertheless, in both cases the singularity is 'good' according to the criterion of [11] since the scalar potential (4.24) is bounded from above, not only on-shell but even off-shell. Accordingly, in both cases, the presence of the singularity signals some genuine IR phenomenon in the dual field theory.…”

“…This though does not exclude the possibility that, non-perturbatively in φ, W (φ; α) and W o (φ) are continuously connected. Remarkably, we will see below in an example where the exact one-parameter family W (φ; α) 11 From now on we drop the subscript D in the gravitational constant κ and the AdS radius l since we will always work in D = 4.…”

“…5 Although one often views fake supergravity as an effective subsector of some gauged supergravity, by identifying both the scalar potential and the fake superpotential of fake supergravity with the true potential and superpotential respectively of the gauged supergravity [4,3,6], we will instead treat fake supergravity as a powerful solution generating technique for non-supersymmetric solutions of a given gauged supergravity. In particular, we will treat (1.8) as a first order non-linear differential equation for the fake superpotential W (φ) [10,11,2,12] (see also [13] where a very similar perspective is adopted). For scalar potentials arising from some gauged supergravity this equation admits at least one solution, namely the true superpotential of the theory.…”