Stability of Hořava-Lifshitz black holes in the context of AdS/CFT

Abstract

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes.These black holes are subjected to stringy effects that might render them unstable. Hořava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Hořava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Hořava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in λ = 1 Hořava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter ǫ close to unity. Sufficiently charged flat black holes for ǫ close to unity, and sufficiently charged positively curved black holes with ǫ close to zero, are also unstable. The implication to the Hořava-Lifshitz holographic superconductor is discussed.

Charged dilatonic black holes in gravity’s rainbow

“…In the IR limit this gravity reduces to general relativity, and so it can be considered as a UV completion of general relativity. Motivated by this work on Horava-Lifshitz gravity, different Lifshitz scalings for space and time have been considered for type IIA string theory [3], type IIB string theory [4], the AdS/CFT correspondence [5][6][7][8], dilatonic black branes [9,10], and dilatonic black holes a e-mail: hendi@shirazu.ac.ir b e-mail: f2mir@uwaterloo.ca c e-mail: behzad.eslampanah@gmail.com d e-mail: sh.panahiyan@gmail.com [11,12]. Another UV completion theory of general relativity which reduces to general relativity in the IR limit is called gravity's rainbow [13].…”

Dilatonic black holes in gravity’s rainbow with a nonlinear source: the effects of thermal fluctuations

“…Horava-Lifshitz gravity [3] is one of the interesting UV modifications of general relativity (GR), in which reduces to GR at infrared (IR) limit. Based on Lifshitz scaling for space and time, different attractive subjects have been considered such as string theory of types IIA and IIB [4,5], AdS/CFT correspondence [6][7][8], dilatonic black holes/branes [9][10][11][12][13] and phase transitions/geometrical thermodynamics of black holes [14][15][16].…”

Charged scalar quasi-normal modes for higher-dimensional Born–Infeld dilatonic black holes with Lifshitz scaling

“…Thus, QNMs of a higher dimensional AdS black hole can be used to describe the behavior of strongly coupled quark-gluon plasmas [62,63]. As the AdS/CFT correspondence has been used to analyze the CFT dual to a Lifshitz AdS spacetime [64,65], it would be interesting to repeat the analysis done in this paper, for an asymptotically AdS black hole. Then such QNMs can be used to analyze various properties of CFT dual to such a black hole in the Lifshitz AdS spacetime.…”