# Stability of Horava-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. Horava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attention due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Horava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Horava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in {lambda} = 1 Horava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter {epsilon} close to unity. Sufficiently charged flat black holes for {epsilon} close to unity, and sufficiently charged positively curved black holes with {epsilon} close to zero, are also unstable. The implication to the Horava-Lifshitz holographic superconductor is discussed.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1043205

- Report Number(s):
- SLAC-PUB-15016

Journal ID: ISSN 1550-7998; arXiv:1106.3555; TRN: US1203026

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 10; Journal ID: ISSN 1550-7998

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; DE SITTER GROUP; FERMI GAS; FIELD THEORIES; QUARK MATTER; STABILITY; SUPERCONDUCTORS; SYMMETRY; TRANSFORMATIONS; Gravitation and Cosmology, Theory-HEP,HEPTH, GRQC

### Citation Formats

```
Ong, Yen Chin, /Taiwan, Natl. Taiwan U., Chen, Pisin, and /Taiwan, Natl. Taiwan U. /KIPAC, Menlo Park /SLAC.
```*Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT*. United States: N. p., 2012.
Web.

```
Ong, Yen Chin, /Taiwan, Natl. Taiwan U., Chen, Pisin, & /Taiwan, Natl. Taiwan U. /KIPAC, Menlo Park /SLAC.
```*Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT*. United States.

```
Ong, Yen Chin, /Taiwan, Natl. Taiwan U., Chen, Pisin, and /Taiwan, Natl. Taiwan U. /KIPAC, Menlo Park /SLAC. Wed .
"Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT". United States. https://www.osti.gov/servlets/purl/1043205.
```

```
@article{osti_1043205,
```

title = {Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT},

author = {Ong, Yen Chin and /Taiwan, Natl. Taiwan U. and Chen, Pisin and /Taiwan, Natl. Taiwan U. /KIPAC, Menlo Park /SLAC},

abstractNote = {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. Horava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attention due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Horava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Horava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in {lambda} = 1 Horava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter {epsilon} close to unity. Sufficiently charged flat black holes for {epsilon} close to unity, and sufficiently charged positively curved black holes with {epsilon} close to zero, are also unstable. The implication to the Horava-Lifshitz holographic superconductor is discussed.},

doi = {},

journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

issn = {1550-7998},

number = 10,

volume = 84,

place = {United States},

year = {2012},

month = {6}

}