CDT meets Hořava–Lifshitz gravity

The theory of causal dynamical triangulations (CDT) attempts to define a nonperturbative theory of quantum gravity as a sum over spacetime geometries. One of the ingredients of the CDT framework is a global time foliation, which also plays a central role in the quantum gravity theory recently formulated by Ho?ava. We show that the phase diagram of CDT bears a striking resemblance with the generic Lifshitz phase diagram appealed to by Ho?ava. We argue that CDT might provide a unifying nonperturbative framework for anisotropic as well as isotropic theories of quantum gravity.     

Lifshitz black holes in the Hořava–Lifshitz gravity

We investigate the Lifshitz black holes from the Ho?ava–Lifshitz gravity by comparing with the Lifshitz black hole from the 3D new massive gravity. We note that these solutions all have single horizons. These black holes are very similar to each other when studying their thermodynamics. It is shown that a second order phase transition is unlikely possible to occur between z=3,2$z=3,2$ Lifshitz black holes and z=1$z=1$ Ho?ava black hole.     

Generalized uncertainty principle and Hořava–Lifshitz gravity

We explore a connection between generalized uncertainty principle (GUP) and modified Ho?ava–Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Ho?ava–Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the p⁵$p^5$-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.     

T-duality for string in Hořava–Lifshitz gravity

We continue our study of the Lorentz-breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze the properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz-breaking string theories and show that they are the same as that of Buscher’s T-duality for the relativistic strings.     

Thermodynamics of black holes in Hořava–Lifshitz gravity

By using the canonical Hamiltonian method, we obtain the mass and entropy of the black holes with general dynamical coupling constant λ in Ho?ava–Lifshitz Gravity. Regardless of whether the horizon is sphere, plane or hyperboloid, we find these black holes are thermodynamically stable in some parameter space and unstable phase also exists in other parameter space. The relation between the entropy and horizon area of the black holes has an additional coefficient depending on the coupling constant λ  , compared to the λ=1$\lambda =1$ case. For λ=1$\lambda =1$, the well-known coefficient of one quarter is recovered in the infrared region.     

Extremal black holes in the Hořava–Lifshitz gravity

We study the near-horizon geometry of extremal black holes in the z=3 Ho?ava–Lifshitz gravity with a flow parameter λ. For λ>1/2, near-horizon geometry of extremal black holes are AdS ₂×S ² with different radii, depending on the (modified) Ho?ava–Lifshitz gravity. For 1/3≤λ≤1/2, the radius v ₂ of S ² is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein–Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein–Hawking entropy of extremal black holes.     

Hořava–Lifshitz dark energy

We formulate Ho?ava–Lifshitz cosmology with an additional scalar field that leads to an effective dark energy sector. We find that, due to the inherited features from the gravitational background, Ho?ava–Lifshitz dark energy naturally presents very interesting behaviors, possessing a varying equation-of-state parameter, exhibiting phantom behavior and allowing for a realization of the phantom divide crossing. In addition, Ho?ava–Lifshitz dark energy guarantees for a bounce at small scale factors and it may trigger the turnaround at large scale factors, leading naturally to cyclic cosmology.     

Slowly rotating black holes in the Hořava–Lifshitz gravity

We investigate slowly rotating black holes in the Ho?ava–Lifshitz (HL) gravity. For Λ _W =0 and λ=1, we find a slowly rotating black hole of the Kehagias–Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.     

Hamiltonian analysis of linearized extension of Hořava–Lifshitz gravity

We investigate the Hamiltonian structure of linearized extended Ho?ava–Lifshitz gravity in a flat cosmological background following the Faddeev–Jackiw's Hamiltonian reduction formalism. The Hamiltonian structure of extended Ho?ava–Lifshitz gravity is similar to that of the projectable version of original Ho?ava–Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. In the infrared (IR) limit, however, there is one propagating degree of freedom in the general cosmological background, and that is coupled to the scalar graviton mode. We find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the IR limit. But it is necessary to go beyond linear order in order to draw any conclusion of the strong coupling problem.     

Nonpropagation of scalar in the deformed Hořava–Lifshitz gravity

We study the propagation of a scalar, the trace of h_ij$h_{ij}$ in the deformed Ho?ava–Lifshitz gravity with coupling constant λ. It turns out that this scalar is not a propagating mode in the Minkowski spacetime background. In this work, we do not choose a gauge-fixing to identify the physical degrees of freedom and instead, make it possible by substituting the constraints into the quadratic Lagrangian.     

Thermodynamics of black holes in the deformed Hořava–Lifshitz gravity

We study thermodynamics of black holes in the deformed Ho?ava–Lifshitz gravity with coupling constant λ  . For λ=1$\lambda =1$, the black hole behaves the Reissner–Norström black hole. Hence, this is different from the Schwarzschild black hole of Einstein gravity. A connection to the generalized uncertainty principle is explored to understand the Ho?ava–Lifshitz black holes.     

Hawking radiation and black hole spectroscopy in Hořava–Lifshitz gravity

Hawking radiation from the black hole in Ho?ava–Lifshitz gravity is discussed by a reformulation of the tunneling method given in Banerjee and Majhi (2009) [17]. Using a density matrix technique the radiation spectrum is derived which is identical to that of a perfect black body. The temperature obtained here is proportional to the surface gravity of the black hole as occurs in usual Einstein gravity. The entropy is also derived by using the first law of black hole thermodynamics. Finally, the spectrum of entropy/area is obtained. The latter result is also discussed from the viewpoint of quasi-normal modes. Both methods lead to an equispaced entropy spectrum, although the value of the spacing is not the same. On the other hand, since the entropy is not proportional to the horizon area of the black hole, the area spectrum is not equidistant, a finding which also holds for the Einstein–Gauss–Bonnet theory.     

Thermodynamics of Hořava–Lifshitz black holes

We study black holes in the Ho?ava–Lifshitz gravity with a parameter λ. For 1/3≤λ<3, the black holes behave the Lifshitz black holes with dynamical exponent 0<z≤4, while for λ>3, the black holes behave the Reissner–Nordström type black hole in asymptotically flat spacetimes. Hence, these all are quite different from the Schwarzschild–AdS black hole of Einstein gravity. The temperature, mass, entropy, and heat capacity are derived for investigating thermodynamic properties of these black holes.     

Phenomenological aspects of Hořava–Lifshitz cosmology

We show that, assuming the dispersion relation proposed recently by Ho?ava in the context of quantum gravity, radiation energy density exhibits a peculiar dependence on the scale factor; the radiation energy density decreases proportional to a⁻⁶$a^{\mathrm{-6}}$. This simple scaling can have an impact on cosmology. As an example, we show that the resultant baryon asymmetry as well as the stochastic gravity waves can be enhanced. We also discuss current observational constraint on the dispersion relation.     

Primordial perturbation in Hořava–Lifshitz cosmology

Recently, Ho?ava has proposed a renormalizable theory of gravity with critical exponent z=3$z=3$ in the UV. This proposal might imply that the scale invariant primordial perturbation can be generated in any expansion of early universe with a∼tn$a\sim t^n$ and n>1/3$n>1/3$, which, in this Letter, will be confirmed by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. It is found that if enough efolding number of primordial perturbation suitable for observable universe is required, then n?1$n?1$ needs to be satisfied, unless the scale of UV regime is quite low. However, the possible UV completeness of HL gravity helps to relax this bound.     

Hawking radiation of black holes in infrared modified Hořava–Lifshitz gravity

We study the Hawking radiation of spherically symmetric, asymptotically flat black holes in the infrared modified Ho?ava–Lifshitz gravity by applying the methods of covariant anomaly cancelation and effective action, as well as the approach of Damour–Ruffini–Sannan’s. These black holes behave as the usual Schwarzschild ones of general relativity when the radial distance is very large. We also extend the method of covariant anomaly cancelation to derive the Hawking temperature of the spherically symmetric, asymptotically AdS black holes that represent the analogues of the Schwarzschild AdS ones.     

Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant

We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M$M$ and radius R$R$. To this end, we take into account a static and spherically symmetric solution of Ho?ava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.     

Modified dispersion relations in Hořava–Lifshitz gravity and Finsler brane models

We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein–Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Hořava–Lifshitz, HL, and/or Einstein’s general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Hořava–Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.     

Lagrange multiplier modified Ho?ava–Lifshitz gravity

We consider RFDiff invariant Hořava–Lifshitz gravity action with additional Lagrange multiplier term that is a function of scalar curvature. We find its Hamiltonian formulation and we show that the constraint structure implies the same number of physical degrees of freedom as in General Relativity.