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.     

Towards constraining of the Horava–Lifshitz gravities

Recently a renormalizable model of gravity has been proposed, which might be a UV completion of General Relativity (GR) or its infra-red modification, probably with a strongly coupled scalar mode. Although the generic vacuum of the theory is anti-de Sitter one, particular limits of the theory allow for the Minkowski vacuum. In this limit (though without consideration of the strongly coupled scalar field) post-Newtonian coefficients of spherically symmetric solutions coincide with those of the General Relativity. Thus the deviations from the convenient GR should be tested beyond the post-Newtonian corrections, that is for a system with strong gravity at astrophysical scales. In this Letter we consider potentially observable properties of black holes in the deformed Horava–Lifshitz gravity with Minkowski vacuum: the gravitational lensing and quasinormal modes. We have showed that the bending angle is seemingly smaller in the considered Horava–Lifshitz gravity than in GR. The quasinormal modes of black holes are longer lived and have larger real oscillation frequency in the Horava–Lifshitz gravity than in GR. These corrections should be observable in the near future experiments on lensing and by gravitational antennas, helping to constrain parameters of the Horava–Lifshitz gravity or to discard it.     

A Classical String in Lifshitz–Vaidya Geometry

We study the time evolution of the expectation value of a rectangular Wilson loop in strongly anisotropic time-dependent plasma using gauge-gravity duality. The corresponding gravity theory is given by describing time evolution of a classical string in the Lifshitz–Vaidya background. We show that the expectation value of the Wilson loop oscillates about the value of the static potential with the same parameters after the energy injection is over. We discuss how the amplitude and frequency of the oscillation depend on the parameters of the theory. In particular, for the transverse case, by raising the anisotropy parameter, we observe that the amplitude and frequency of the oscillation increase. In the longitudinal case, although the amplitude of the oscillation increases for larger values of anisotropy parameter, the frequency is independent of anisotropy parameter.     

Particle acceleration in Horava–Lifshitz black holes

In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava–Lifshitz black hole. For the case of a slowly rotating KS solution of Horava–Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for static black holes and unlimited value of the center-of-mass energy for rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles. In this limit the center-of-mass energy of two colliding particles in the neighborhood of the rotating Horava–Lifshitz black hole could be arbitrarily high. We found appropriate conditions where the critical angular momentum could have an orbit outside the horizon. Finally, we obtain the center-of-mass energy corresponding to this circle orbit.     

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.     

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.     

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.     

二级相变理论和Lifshitz条件不成立的论证

系统的自由能是序参量的泛函。在二级相变点附近,自由能密度是序参量及其关联项的幂次展式。按本文给定的方法,无论关联项是定域还是非定域的,由对自由能的一级变分等于零,都能求得表示平衡态位形的序参量。在求解过程,必须将序参量进行傅氏变换,这与序参量以系统对称群的基函数展开是一致的,由此对二级相变中对称改变进行了分析。利用变分法中极值的充要条件(或充分条件),我们讨论了二级相变过程中状态的稳定性条件。由于我们对自由能求极值时没有略去关联项,因此不存在Lifshitz的对称改变限制条件。这里强调指出:实质上,Lif     

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.     

Calculation of Free Energy of the Integrable Landau—Lifshitz model

The generalized Bethe-ansatz method of thermodynamic analysis of integrable systems was employed to compute the free energy of a classical integrable model,i.e.the Landau-Lifshitz model.Using the action-angle variables of the model and by imposing a periodic boundary condition.we derive a phase-shifted density of states for the excitations of the system.The free energy,in the thermodynamic limit,can be expressed analytic in terms of two coupled nonlinear integral equations of the finie temperature excited energy for effective phonons and kinks (antikinks).we solve these equations iteratively for a special case that the model is in the limit of anisotropic strong yz coupling.     

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.     

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.     

Lifshitz时空s波超导模型的关联长度和穿透深度

在D=d+2维各向异性的Lifshitz黑洞时空背景中, 在探子极限下, 用解析方法研究了临界温度附近引力系统的微扰, 计算出超导的关联长度ξα(1/T_c)(1-(T/T_c)^-1/2, 这与平均场论的结果一致. 进一步, 考虑在该系统中加一个均匀外磁场, 计算出穿透深度λα(T_c-T)^-1/2, 该结果与Ginzburg-Landau理论相符.     

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.     

Pressure-induced Lifshitz transition in the type Ⅱ Dirac semimetal PtTe_2

Numerous exotic properties have been discovered in Dirac Semimetals(DSMs) and Weyl Semimetals(WSMs). In a given DSM/WSM, the Dirac/Weyl nodes usually coexist with other bulk states, making their respective contribution elusive. In this work, we distinguish the role of bulk states from the tilted Dirac nodes on the transport properties in DSMs. Specifically, we applied pressure to a type-II DSM material, PtTe2, and studied its pressure modified electronic and lattice structure systematically by using in situ transport measurements and X-ray diffraction(XRD). A pressure-induced transition at about 20 GPa is revealed in the transport properties, while the layered lattice structure is robust against pressure as illustrated in XRD measurement results.Density functional theory(DFT) calculations suggest that this is originated from the Lifshitz transition in the bulk states. Our findings provide evidence to identify the bulk states' influence on transport from the topologically-protected DSM states in the DSM material.     

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.     

Gauss–Bonnet dark energy on Hořava–Lifshitz cosmology

We investigate the Gauss–Bonnet dark energy model and its deformed version on Ho?ava–Lifshitz cosmology, which belongs to the class of cosmologies obtained from the so-called projectable version of Ho?ava–Lifshitz gravity. In particular, we investigate the bulk/boundary interaction in this scenario through the Q function, which we interpret as a measure of the energy transference between the bulk and the spacetime boundary. Then we discuss whether the thermal equilibrium will be stable or not, once it is reached, and the validity of the generalized second law. We show that the Q function can exhibit sign changes along the cosmic evolution and the Universe reaches the thermal equilibrium as a transient phenomenon.