Lattice Black Branes: Sphere Packing in General Relativity

We perturbatively construct asymptotically ${\mathbb{R}}^{1,3}\times {\mathbb{T}}^2$ black branes with multiple inhomogeneous directions and show that some of them are thermodynamically preferred over uniform branes in both the microcanonical and canonical ensembles. This demonstrates that, unlike five-dimensional black strings, the instability of some unstable black branes has a plausible endpoint that does not require a violation of cosmic censorship.