Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent

Gaetano Bertoldi; Benjamin A. Burrington; Amanda Peet

doi:10.1103/PhysRevD.80.126003

paper

Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent

arXiv:0905.3183 · doi:10.1103/PhysRevD.80.126003

Abstract

Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z \geq 1$ . We numerically explore black holes in these backgrounds for a range of values of $z$ . We find drastically different behavior for $z > 2$ and $z < 2$ . We find that for $z > 2$ ( $z < 2$ ) the Lifshitz fixed point is repulsive (attractive) when going to larger radial parameter $r$ . For the repulsive $z > 2$ backgrounds, we find a continuous family of black holes satisfying a finite energy condition. However, for $z < 2$ we find that the finite energy condition is more restrictive, and we expect only a discrete set of black hole solutions, unless some unexpected cancellations occur. For all black holes, we plot temperature $T$ as a function of horizon radius $r_{0}$ . For $z ⪅ 1.761$ we find that this curve develops a negative slope for certain values of $r_{0}$ possibly indicating a thermodynamic instability.

23 pages, 6 figures, references corrected, graphs made readable in greyscale

Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent

Abstract

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