  Both projectable and non-projectable versions of Horava-Lifshitz gravity face
serious challenges. In the non-projectable version, the constraint algebra is
seemingly inconsistent. The projectable version lacks a local Hamiltonian
constraint, thus allowing for an extra scalar mode which can be problematic. A
new formulation of non-projectable Horava-Lifshitz gravity, naturally realized
as a representation of the master constraint algebra studied by loop quantum
gravity researchers, is presented. This yields a consistent canonical theory
with first class constraints. It captures the essence of Horava-Lifshitz
gravity in retaining only spatial diffeomorphisms (instead of full space-time
covariance) as the physically relevant non-trivial gauge symmetry; at the same
time the local Hamiltonian constraint needed to eliminate the extra mode is
equivalently enforced by the master constraint.
