  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 $z\lessapprox 1.761$ we find that this curve
develops a negative slope for certain values of $r_0$ possibly indicating a
thermodynamic instability.
