Membrane Solutions to Horava Gravity

We have investigated purely gravitational membrane solutions to the Horava nonrelativistic theory of gravity with detailed balance in 3 + 1 dimensions. We find that for arbitrary values of the running parameter lambda > 1/3 there exist two branches of membrane solutions, and that in the special case lambda = 1 one of them is degenerate, the lapse function being undetermined. For negative values of the cosmological constant, the solution contains a single membrane sitting at the center of space, which extends infinitely in the transverse direction, approaching a Lifshitz metric. For positive values of the cosmological constant, the solution represents a space that is bounded in the transverse direction, with two parallel membrane-like or point-like singularities sitting at each of the boundaries.