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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Fermionic quasinormal modes for two-dimensional Hořava–Lifshitz black holes

To obtain fermionic quasinormal modes, the Dirac equation for two types of black holes is investigated. It is shown that two different geometries lead to distinctive types of quasinormal modes, while the boundary conditions imposed on the solutions in both cases are identical. For the first type of black hole, the quasinormal modes have continuous spectrum with negative imaginary part that provides the stability of perturbations. For the second type of the black hole, the quasinormal modes have a discrete spectrum and are completely imaginary.     

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.     

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 modified Hořava–Lifshitz (HL) gravity with Λ _W =0 and λ=1. We do this by showing that the Kerr metric does not satisfy the full equations derived from modified HL gravity.     

Area spectrum and thermodynamics of KS black holes in Hořava gravity

We investigate the area spectrum of Kehagias–Sfetsos black hole in Ho?ava–Lifshitz gravity via modified adiabatic invariant $I=\oint p_i d q_i$ I = ∮ p i d q i and Bohr–Sommerfeld quantization rule. We find that the area spectrum is equally spaced with a spacing of $ \Delta A=4 \pi l_p ^2$ Δ A = 4 π l p 2 . We have also studied the thermodynamic behavior of KS black hole by deriving different thermodynamic quantities.     

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.     

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.     

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.     

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.     

Constraining Hořava–Lifshitz gravity from neutrino speed experiments

We constrain Ho?ava–Lifshitz gravity using the results of the OPERA and ICARUS neutrino speed experiments, which show that neutrinos are luminal particles, as found from examining the fermion propagation in the earth’s gravitational field. In particular, investigating the Dirac equation in the spherical solutions of the theory, we find that the neutrinos feel an effective metric with respect to which they might propagate superluminally. Therefore, in demanding not to have superluminal or subluminal motion we constrain the parameters of the theory. Although the excluded parameter regions are very narrow, we find that the detailed balance case lies in the excluded region.     

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.