Lifshitz Topological Black Holes

Abstract

I find a class of black hole solutions to a (3+1) dimensional theory gravity coupled to abelian gauge fields with negative cosmological constant that has been proposed as the dual theory to a Lifshitz theory describing critical phenomena in (2+1) dimensions. These black holes are all asymptotic to a Lifshitz fixed point geometry and depend on a single parameter that determines both their area (or size) and their charge. Most of the solutions are obtained numerically, but an exact solution is also obtained for a particular value of this parameter. The thermodynamic behaviour of large black holes is almost the same regardless of genus, but differs considerably for small black holes. Screening behaviour is exhibited in the dual theory for any genus, but the critical length at which it sets in is genus-dependent for small black holes.

19 pages, 9 figures, Latex

References in corpus (9)

• Quantum Gravity at a Lifshitz Point
• Lectures on holographic methods for condensed matter physics
• Topological Black Holes in Horava-Lifshitz Gravity
• Holographic Renormalization of Asymptotically Flat Spacetimes
• Quantum Criticality and Yang-Mills Gauge Theory
• Formation of Topological Black holes from Gravitational Collapse
• Black holes and non-relativistic quantum systems
• Thermodynamics of Black Holes in Schroedinger Space
• Solitonic Phase Transitions of Galilean Black Holes

Cited by in corpus (15)

• Quantum gravity without Lorentz invariance
• An analytic Lifshitz black hole
• Towards constraining of the Horava-Lifshitz gravities
• A Lifshitz Black Hole in Four Dimensional R^2 Gravity
• Analytic Lifshitz black holes in higher dimensions
• Thermodynamics of black branes in asymptotically Lifshitz spacetimes
• Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries
• Surplus Solid Angle as an Imprint of Horava-Lifshitz Gravity
• Plane symmetric solutions in Horava-Lifshitz theory
• Strong Coupling Quantum Einstein Gravity at a z=2 Lifshitz Point
• Interacting Dark Energy in Hořava-Lifshitz Cosmology
• A Note on Black Holes in Asymptotically Lifshitz Spacetime
• Phase transitions for the Lifshitz black holes
• Holographic Lifshitz Superconductors with an Axion Field
• Constraints on Flows in Horava-Lifshitz Gravity by Classical Solutions