S-branes and (anti-)bubbles in (A)dS space

Abstract

We describe the construction of new locally asymptotically (A)dS geometries with relevance for the AdS/CFT and dS/CFT correspondences. Our approach is to obtain new solutions by analytically continuing black hole solutions. A basic consideration of the method of continuation indicates that these solutions come in three classes: S-branes, bubbles and anti-bubbles. A generalization to spinning or twisted solutions can yield spacetimes with complicated horizon structures. Interestingly enough, several of these spacetimes are nonsingular.

Black strings with a negative cosmological constant: inclusion of electric charge and rotation

“…It is interesting to note that in all considered cases (inclusing the static neutral solutions in [7]), the thermodynamics of the black strings appears to follow the pattern of the corresponding black hole solutions with spherical horizons in AdS backgrounds. On general grounds, one expects the black objects with a boundary topology R×S d−3 ×S 1 to present a richer phase structure than in the usual R × S d−3 case (with R corresponding to the time direction), as the radius of the circle introduces another macroscopic scale in the theory 14 . For example, it is wellknown that Λ = 0 uniform black strings are affected by the Gregory-Laflamme (GL) instability [40].…”

“…In particular, the background metric upon which the dual field theory resides is found by taking the rescaling h ab = lim r→∞ ℓ 2 r 2 γ ab . For k = 1 black 14 Charged bubble solutions can be constructed by taking the analytic continuation z → iu, t → iξ in the general line element (10)…”

How to stop (worrying and love) the bubble: boundary changing solutions

“…Our spherical prolate diagrams are analogs of C-metric diagrams in [31]. Complex ζ ∈ cos −1 [R] is the basis for the skeleton diagrams of [18]. Σ − 2Mr = 0, and ring, Σ + a 2 sin 2 θ = 0, singularity loci in terms of affine coordinates C, Z for the complex plane C 2 .…”

“…If two parallel 5 It should be noted that the Schwarzschild-AdS D bubble grows in a dS D−2 fashion even though the compactified direction grows. The Kerr-AdS D bubble, however, grows at a slower rate [18,33]. soap films are connected to each other then the linking region will grow in size until it feels the effects of the boundary conditions.…”

“…To understand this statement, we recall that S-branes type solutions as well as other time dependent solutions including bubbles of nothing [14,15,16,17,18] can be obtained from (multi-)black hole solutions via analytic continuation. Starting with the D-dimensional Schwarzschild black hole [19] as the canonical example and performing the analytic continuation t → ix D and θ → π/2 + iθ we obtain the bubble of nothing metric…”