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Register a new userScale Invariance in Newton-Cartan and Hov{r}ava-Lifshitz Gravity
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We present a detailed analysis of the construction of $z=2$ and $z eq2$ scale invariant Hov{r}ava-Lifshitz gravity. The construction procedure is based on the realization of Hov{r}ava-Lifshitz gravity as the dynamical Newton-Cartan geometry as well as a non-relativistic tensor calculus in the presence of the scale symmetry. An important consequence of this method is that it provides us the necessary mechanism to distinguish the local scale invariance from the local Schrodinger invariance. Based on this result we discuss the $z=2$ scale invariant Hov{r}ava-Lifshitz gravity and the symmetry enhancement to the full Schrodinger group.
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We investigate string-like solutions in four dimensions based on Hov{r}ava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black strings are solutions in Hov{r}ava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the conformal lapse function is not constrained in Hov{r}ava-Lifshitz gravity. It turns out that if $lambda e 1$, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., $lambda=1$), there exists an additional solution of which the conformal lapse function is determined. Interestingly, this solution admits a uniform BTZ black string along the string direction, which is distinguished from the warped BTZ black string in Einstein gravity. Therefore, it is a good candidate for the test of the theory.
We study holographic superconductors in a Hov{r}ava-Lifshitz black hole without the condition of the detailed balance. We show that it is easier for the scalar hair to form as the parameter of the detailed balance becomes larger, but harder when the mass of the scalar field larger. We also find that the ratio of the gap frequency in conductivity to the critical temperature, $omega_{g}/T_c$, almost linear decreases with the increase of the balance constant. For $epsilon= 0$ the ratio reduces to Cais result $omega_g/T_capprox 13$ found in the Hov{r}ava-Lifshitz black hole with the condition of the detailed balance, while as $epsilon rightarrow 1$ it tends to Horowitz-Roberts relation $omega_g/T_capprox 8$ obtained in the AdS Schwarzschild black hole. Our result provides a bridge between the results for the Hv{o}rava-Lifshitz theory with the condition of the detailed balance and Einsteins gravity.
We investigate the Hamiltonian structure of linearized extended Hov{r}ava- Lifshitz gravity in a flat cosmological background following the Faddeev-Jackiws Hamiltonian reduction formalism. The Hamiltonian structure of extended Hov{r}ava-Lifshitz gravity is similar to that of the projectable version of original Hov{r}ava-Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. We also find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the infrared (IR) limit, but it is coupled to the matter field in a general cosmological background. But it is necessary to go beyond linear order in order to draw any conclusion of the strong coupling problem.
We show how Einstein-Cartan gravity can accommodate both global scale and local scale (Weyl) invariance. To this end, we construct a wide class of models with nonpropagaing torsion and a nonminimally coupled scalar field. In phenomenological applications the scalar field is associated with the Higgs boson. For global scale invariance, an additional field --- dilaton --- is needed to make the theory phenomenologically viable. In the case of the Weyl symmetry, the dilaton is spurious and the theory reduces to a sub-class of one-field models. In both scenarios of scale invariance, we derive an equivalent metric theory and discuss possible implications for phenomenology.
In this paper we study the corrections emergent from a Hov{r}ava-Lifshitz extension of the complex scalar sector to the Bose-Einstein condensation and to the thermodynamics parameters. We initially discussed some features of the model to only then compute the corrections to the Bose-Einstein condensation. The calculations were done by computing the generating functional, from which we extract the thermodynamics parameters. We also obtained the Lifshitz scaling correction for the critical temperature $T_c$ that sets the Bose-Einstein Condensation.
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