Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity

Abstract

We investigate static, planar solutions of Einstein-scalar gravity admitting an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is positive and the scalar potential can be derived from a superpotential, minimum energy theorems indicate the existence of a scalar soliton. On the other hand, for these models, no-hair theorems forbid the existence of hairy black brane solutions with AdS asymptotics. By considering a specific example (an exact integrable model which has the form of a Toda molecule) and by deriving explicit exact solution, we show that these models allow for hairy black brane solutions with non-AdS domain wall asymptotics, whose extremal limit is a scalar soliton. The soliton smoothly interpolates between a non-AdS domain wall solution at r = infinity and an AdS solution near r = 0

Phase transition and hyperscaling violation for scalar black branes

“…The second class of these non-AdS metrics is characterized by breaking of the scale isometry, but the (d+ 1)-dimensional Poincaré invariance is preserved. In the literature they are often referred to as domain wall (DW) solutions [1,26,29,34,35], in analogy with the DW solutions of supergravity (SUGRA) theories.…”

“…In fact, usual no-hair theorems based on the positive energy theorem forbid the existence of black brane (BB) solutions with AdS asymptotics when the squared-mass of the scalar is positive [40][41][42]. However, in a recent paper it has been shown that these no-hair theorems can be circumvented by giving up the condition that the BB solution has AdS asymptotics [1,29]. In Ref.…”

“…In Ref. [1] we have derived exact hairy, asymptotically non-AdS, black brane solutions of a Einstein-scalar gravity model with positive squared mass for the scalar field. We have shown that the extremal limit of these BB solutions is a scalar soliton which interpolates between an AdS vacuum in the near-horizon region and a scale covariant, DW, solution in the asymptotic region.…”

“…[1,10] open up the possibility of realizing an alternative scenario in which the usual roles played by the IR and UV regions are reversed. In the dual QFT, the IR physics is determined by an infrared fixed point, i.e.…”

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We investigate the thermodynamical behavior and the scaling symmetries of the scalar dressed black brane (BB) solutions of a recently proposed, exactly integrable Einstein-scalar gravity model [1], which also arises as compactification of (p−1)-branes with a smeared charge. The extremal, zero temperature, solution is a scalar soliton interpolating between a conformal invariant AdS vacuum in the near-horizon region and a scale covariant metric (generating hyperscaling violation on the boundary field theory) asymptotically.

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