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Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent

2009; American Physical Society; Volume: 80; Issue: 12 Linguagem: Inglês

10.1103/physrevd.80.126003

1550-7998

Gaetano Bertoldi, Benjamin A. Burrington, Amanda W. Peet,

Advanced Mathematical Physics Problems

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 $z\ensuremath{\ge}1$. 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.