Lifshitz Gravity Research Articles

Geometrothermodynamics in Hořava–Lifshitz gravity

We investigate the thermodynamic geometries of the most general static, spherically symmetric, topological black holes of the Hořava–Lifshitz gravity. In particular, we show that a Legendre invariant metric derived in the context of geometrothermodynamics for the equilibrium manifold correctly reproduces the phase transition structure of these black holes. Moreover, the limiting cases in which the mass, entropy or Hawking temperature vanish are also accompanied by curvature singularities which indicate the limit of applicability of the thermodynamics and geometrothermodynamics of black holes. The Einstein limit and the case of a black hole with a flat horizon are also investigated.

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.

The absence of the Kerr black hole in the Hořava–Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Ho\v{r}ava-Lifshitz (HL) gravity with $\Lambda_W=0$ and $\lambda=1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.

On the motion of particles in covariant Hořava–Lifshitz gravity and the meaning of the A-field

We studied the low energy motion of particles in the general covariant version of Hořava–Lifshitz gravity proposed by Hořava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Hořava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newtonʼs gravity law even in the weak gravitational field approximation.

Spherically symmetric solutions, Newton’s Law, and the infrared limitλ→1in covariant Horava-Lifshitz gravity

In this note we examine whether spherically symmetric solutions in Covariant Horava Lifshitz Gravity can reproduce Newton's Law in the IR limit \lambda->1. We adopt the position that the auxiliary field A is independent of the space-time metric [10,11], and we assume, as in [4], that $\lambda$ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit \lambda->1, unless \lambda does not run, and has the fixed value \lambda=1. Finally, we comment on the Horava and Melby Thompson approach [4] in which A is assumed as a part of the space-time metric in the IR.

A Note on Friedmann Equation of FRW Universe in Deformed Hořava—Lifshitz Gravity from Entropic Force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann—Robertson—Walker universe for the deformed Hořava—Lifshitz gravity. It is shown that, when the parameter of Hořava—Lifshitz gravity ω → ∞, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hořava—Lifshitz gravity.

On a spectral geometry approach to Hořava–Lifshitz gravity: a spectral dimension

We initiate the study of Hořava–Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of spacetime. It is shown that for the natural choice of a Dirac operator (or rather corresponding generalized Laplacian), which respects both the foliation structure and anisotropic scaling, the result of Hořava on a spectral dimension is reproduced for an arbitrary, non-flat spacetime. The advantage and further applications of our approach are discussed.

Matter couplings in Hořava–Lifshitz theories and their cosmological applications

In this paper, the issue of how to introduce matter in Hořava–Lifshitz theories of gravity is addressed. This is a key point in order to complete the proper definition of these theories and, more importantly, to study their possible phenomenological implications. As is well known, in Hořava–Lifshitz gravity, the breakdown of Lorentz invariance invalidates the usual notion of minimally coupled matter. Two different approaches to bypass this problem are described here. One is based on a Kaluza–Klein reinterpretation of the 3+1 decomposition of the gravity degrees of freedom, which naturally leads to a definition of a U(1) gauge symmetry and, hence, to a new type of minimal coupling. The other approach relies on a midi-superspace formalism and the subsequent parametrization of the matter stress–energy tensor in terms of deep infrared variables. Using the last option, the phase space of Hořava–Lifshitz cosmology in the presence of general matter couplings is studied. It is found, in particular, that the equation of state of the effective matter may be very different from the actual matter one, owing to the nonlinear interactions which exist between matter and gravity.

ASPECTS OF HOŘAVA–LIFSHITZ COSMOLOGY

We review some general aspects of Hořava–Lifshitz cosmology. Formulating it in its basic version, we extract the cosmological equations and we use observational data in order to constrain the parameters of the theory. Through a phase–space analysis we extract the late-time stable solutions, and we show that bouncing and cyclic behavior can arise naturally. Concerning the effective dark energy sector we show that it can describe the phantom phase without the use of a phantom field. However, performing a detailed perturbation analysis, we see that Hořava–Lifshitz gravity in its basic version, suffers from instabilities. Therefore, suitable generalizations are required in order for this novel theory to be a candidate for the description of nature.

EVOLUTION OF ELECTROMAGNETIC AND DIRAC PERTURBATIONS AROUND A BLACK HOLE IN HOŘAVA GRAVITY

The evolution of electromagnetic and massless Dirac perturbations in the spacetime geometry of Kehagias–Sfetsos (KS) black hole in the deformed Hořava–Lifshitz (HL) gravity is investigated and the associated quasinormal modes (QNMs) are evaluated from time domain integration data. We find a considerable deviation in the nature of field evolution in HL theory from that in the Schwarzschild spacetime and QNM region extends over a longer time in HL theory before the power-law tail decay begins. The dependence of the field evolution on the HL parameter α is also studied. In the time domain picture we find that the length of QNM region increases with α. But the late-time decay of field follows the same power-law tail behavior as in the case of Schwarzschild black hole.

THERMODYNAMICAL LAWS IN HOŘAVA–LIFSHITZ GRAVITY

In this work, we investigate the validity of the GSL of thermodynamics in the universe (open, closed and flat) governed by Hořava–Lifshitz (HL) gravity. If the universe contains barotropic fluid, we obtain the corresponding solutions. The validity of the GSL is examined by two approaches: (i) the robust approach and (ii) the effective approach. In the robust approach, we consider that the universe contains only matter fluid. Also, the effect of the gravitational sector of HL gravity is incorporated through the modified black hole entropy on the horizon. The effective approach is that all extra information of HL gravity is cast into an effective dark energy fluid, and so we consider that the universe contains matter fluid plus this effective fluid. This approach is essentially the same as Einstein's gravity theory. The general prescription for the validity of the GSL is discussed. Graphically, we show that the GSL may be satisfied for the open, closed and flat universes on the different horizons with different conditions.

Horava–Lifshitz gravity: calculation of radar signal delay contribution in the vicinity of the Sun in the Kehagias–Sfetsos solution

There has been a renewed interest in the recent years for the study of gravitational theories alternative to General Relativity (GR). This results from current observations that seem to question the role of General Relativity theory at large distances, i.e., galactic and cosmological ones. An example of such theories is that of Modified Newtonian Dynamics or (MOND). In an effort for a description of gravitation in a quantum framework Horava has recently proposed the Horava–Lifshitz gravity (HL). Our goal is to study the effect of radar signal delays in the vicinity of the sun for the Kehagias–Sfetsos space-time solution of the Horava–Lifshitz modified gravity. For that we use a spherically symmetric modified solar system space-time metric and we calculate the radar signal delay correction as a function of the non-dimensional HL parameter ψ. Next expressing ψ as a function of the planetary orbital elements we derive an expression for the Kehagias–Sfetsos radar time delay solution, which next calculate for all the planets in the solar system excluding Pluto. Finally, for the planets Mercury to Neptune, we obtain radar time delays in the range of \(531\times 10^{-9}~\mathrm{ps} \le t_{\mathit{KS}_{\mathit{MER}}} \le 5379.86~\mathrm{ps}\) for the planets Mercury to Neptune.

Quasitopological Lifshitz black holes

We investigate the effects of including a quasi-topological cubic curvature term to the Gauss-Bonnet action to five dimensional Lifshitz gravity. We find that a new set of Lifshitz black hole solutions exist that are analogous to those obtained in third-order Lovelock gravity in higher dimensions. No additional matter fields are required to obtain solutions with asymptotic Lifshitz behaviour, though we also investigate solutions with matter. Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.

A comparison of Hořava–Lifshitz gravity and Einstein gravity through thin-shell wormhole construction

In this paper, we have constructed a new class of thin-shell wormholes from black holes in Hořava–Lifshitz gravity. Particular emphasis is placed on those aspects that allow a comparison of Hořava–Lifshitz gravity to Einstein gravity. The former enjoys a number of advantages for small values of the throat radius.

Coupling of Brans–Dicke scalar field with Horava–Lifshitz gravity

We look for a Brans–Dicke type generalization of Horava–Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the low energy limit to the usual Brans–Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous, isotropic cosmology and study the effects of the new terms appearing in the model.

Lower-dimensional Hořava–Lifshitz gravity

We consider Horava-Lifshitz gravity in both 1+1 and 2+1 dimensions. These lower-dimensional versions of Horava-Lifshitz gravity are simple enough to be explicitly tractable, but still complex enough to be interesting. We write the most general (non-projectable) action for each case and discuss the resulting dynamics. In the 1+1 case we utilize the equivalence with 2-dimensional Einstein-aether theory to argue that, even though non-trivial, the theory does not have any local degrees of freedom. In the 2+1 case we show that the only dynamical degree of freedom is a scalar, which qualitatively has the same dynamical behaviour as the scalar mode in (non-projectable) Horava-Lifshitz gravity in 3+1 dimensions. We discuss the suitability of these lower-dimensional theories as simpler playgrounds that could help us gain insight into the 3+1 theory. As special cases we also discuss the projectable limit of these theories. Finally, we present an algorithm that extends the equivalence with (higher order) Einstein-aether theory to full Horava-Lifshitz gravity (instead of just the low energy limit), and we use this extension to comment on the apparent naturalness of the covariant formulation of the latter.

New formulation of Horava–Lifshitz quantum gravity as a master constraint theory

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.

Fermion analysis of IR modified Hořava–Lifshitz gravity: tunneling and perturbation perspectives

In this paper, we investigate the fermion Hawking radiation and quasinormal (QN) modes in infrared (IR) modified Hořava–Lifshitz (HL) gravity under tunneling and perturbation perspectives. Firstly, through the fermion tunneling in IR modified HL gravity, we obtain the Hawking radiation emission rate, tunneling temperature and entropy for the Kehagias–Sfetsos black hole. It is found that the results of fermion tunneling are consistent with the thermodynamics results obtained by calculating surface gravity. Secondly, we numerically calculate the low-lying QN mode frequencies of fermion perturbations by using WKB formulas including the third-order and sixth-order approximations simultaneously. It turns out that the actual frequency of fermion perturbation is larger than that in the Schwarzschild case, and the damping rate is smaller than that for the pure Schwarzschild. The results of fermion perturbation suggest the QN modes could live longer in HL gravity.

QUANTUM FIELDS WITH MODIFIED DISPERSION RELATIONS IN CURVED SPACES

We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

Bounce scenarios in the Sotiriou–Visser–Weinfurtner generalization of the projectable Horava–Lifshitz gravity

The occurrence of a bounce in the FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Hořava–Lifshitz (HL) theory of gravity, which includes a ‘dark radiation’ term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the ‘detailed-balance’ condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents a comparison of the phase structure of the original and modified Hořava cosmology. Special attention is paid to the analysis of a wide range of the bouncing solution, appearing in both versions of the Hořava theory.