Abstract
Solutions of Hořava gravity that are asymptotically Lifshitz are explored. General near boundary expansions allow the calculation of the mass of these spacetimes via a Hamiltonian method. Both analytic and numeric solutions are studied which exhibit a causal boundary called the universal horizon, and are therefore black holes of the theory. The thermodynamics of an asymptotically Anti-de Sitter Hořava black hole are verified.
Highlights
Asymptotically approach the novel structure of Lifshitz spacetimes
In GR the Schwarzschild solution can be found this way by expanding about asymptotically flat space: the free constant in the power series solution corresponds to its mass
The class of solutions to Horava gravity that asymptote to Lifshitz spacetimes are explored
Summary
Horava gravity is an alternate theory of gravity [1]. Like general relativity, its low energy behavior can be expressed in the context of geometry. The preferred global time of Horava gravity means that Lorentzian coordinate changes that mix spatial directions into a new time coordinate are no longer allowed. These would alter the notion of which events are simultaneous and violate the preferred foliation of the manifold. Because of the fundamental foliation of spacetime a preferred notion of time exists in Horava gravity and Lorentz symmetry is broken This allows temporal and spatial coordinates to have different mass dimensions and is captured by the dynamical critical exponent zH : [xI ] = −1 while [t] = −zH , implying [GH ] = zH − D.
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