Conformal Anisotropic Mechanics and Hořava gravity

Abstract

In this paper we implement scale anisotropic transformations in the space-time in classical mechanics. The resulting system is consistent with the dispersion relation of gravity at a Lifshitz point recently considered in [9]. Also, we show that our model is a generalization of the conformal mechanics of Alfaro, Fubini and Furlan. For arbitrary z we construct the dynamical symmetries that correspond to the Schroedinger algebra. Furthermore, we obtain the Boltzman distribution for a gas of free particles compatible with anisotropic scaling transformations and compare our result with the corresponding thermodynamics of the recent anisotropic black branes proposed in [8].

T-duality for string in Hořava–Lifshitz gravity

“…We see that the Hamiltonian constraint (2.2) is characterized by the presence of two functions F and G. As in [52,56,57,58,59,60] we presume that F (A) has the form F (A) = A + z n=2 λ n A n with z being the critical exponent of the Hořava-Lifshitz gravity. It is believed that in the IR limit the Hořava-Lifshitz gravity reduces to the ordinary General Relativity when z = 1.…”

“…The basic idea of this Lorentz breaking Hamiltonian formalism is that time and spatial components of momenta are treated differently. Indeed in [51] the construction of a new string theory, called Lorentz-breaking string theory (LBS) has been studied extensively by generalizing the point particle dynamics [52,56,57,58,59,60] in Hořava-Lifshitz gravity. The basic idea of the construction of the LBS theory is following.…”

“…We start with the Hamiltonian formulation of two dimensional theory when the Hamiltonian is linear combination of two constraints: the spatial diffeomorphism constraint and Hamiltonian constraint. As opposite to the Hamiltonian formulation of Polyakov string we consider the Hamiltonian constraint that breaks the Lorentz invariance of the target space-time in the similar way as in the point particle case [52,56,57,58,59,60]. However as opposite to the point particle case now the world-sheet modes depend on spatial coordinate of world-sheet theory so that it is possible to define many LBS theories that reduce to the point particle Hamiltonian constraint [52,56,57,58,59,60] in case of the world-sheet dimensional reduction.…”

Spherically symmetric solutions in Hořava-Lifshitz gravity and their properties

“…Several aspects of the Kehagias-Sfetsos action were analyzed in the literature: cosmological solutions [10,11,12,13], possible tests [14,15,16,17,18], fundamental aspects of the theory [19,20,21,22,23,24,25,26,27,28], black hole solutions (with vanishing shift variables) [29,30,31,32,33,34,35,36,37,38,39,40], special cases such as λ = 1/3 [41] and possible extensions [42,43]. In particular Kiritsis and Kofinas in [38] studied more general solutions considering the Hořava-Lifshitz action with generic (independent) coupling constants, that is, an action not derived from a detailed balance condition.…”

“…Here we are considering the usual relativistic matter term, although in principle it may be possible to consider a deformed term that is gauge invariant (for more general interactions terms see[24,25,26,27,28]). …”