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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Dynamical perturbations and critical phenomena in Gauss–Bonnet AdS black holes

We investigate the perturbations of charged scalar field in 5-dimensional Gauss–Bonnet AdS black hole backgrounds. From the perturbation behaviors we obtain the objective picture on how the high curvature influences the spacetime perturbation and the condensation of the scalar hair. The high curvature effects can also be read from the linear response function such as the susceptibility and the correlation length, when the system approaches the critical point. We find that the Gauss–Bonnet term does not affect the critical exponents of the system and they still take the mean-field values.     

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norstr?m-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.     

Universal properties of distorted Kerr–Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein–Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr–Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.     

Photon emission of extremal Kerr–Newman black holes

In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr–Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained.     

Quasinormal resonances of near-extremal Kerr–Newman black holes

We study analytically   the fundamental resonances of near-extremal, slowly rotating Kerr–Newman black holes. We find a simple analytic expression for these black-hole quasinormal frequencies in terms of the black-hole physical parameters: ω=mΩ−2iπTBH(l+1+n)$\omega =m\Omega -2i\pi T_{\mathrm{BH}}(l+1+n)$, where TBH$T_{\mathrm{BH}}$ and Ω are the temperature and angular velocity of the black hole. The mode parameters l and m   are the spheroidal harmonic index and the azimuthal harmonic index of a co-rotating mode, respectively. This analytical formula is valid in the regime ℑω?ℜω?M⁻¹$\Im \omega ?\Re \omega ?M^{\mathrm{-1}}$, where M is the black-hole mass.     

Topological Born–Infeld-dilaton black holes

We construct a new analytic solution of Einstein–Born–Infeld-dilaton theory in the presence of Liouville-type potentials for the dilaton field. These solutions describe dilaton black holes with nontrivial topology and nonlinear electrodynamics. Black hole horizons and cosmological horizons in these spacetimes, can be a two-dimensional positive, zero or negative constant curvature surface. The asymptotic behavior of these solutions are neither flat nor (A)dS. We calculate the conserved and thermodynamic quantities of these solutions and verify that these quantities satisfy the first law of black hole thermodynamics.     

Tunneling across dilaton–axion black holes

In this work we study both charged and uncharged particles tunneling across the horizon of spherically symmetric dilaton–axion black holes using Parikh–Wilczek tunneling formalism. Such black hole solutions have much significance in string theory based models. For different choices of the dilaton and axion couplings with the electromagnetic field, we show that the tunneling probability depends on the difference between initial and final entropies of the black hole. Our results, which agree with similar results obtained for other classes of black holes, further confirm the usefulness of Parikh–Wilczek formalism to understand Hawking radiation. The emission spectrum is shown to agree with a purely thermal spectrum only in the leading order. The modification of the proportionality factor in the area–entropy relation in the Bekenstein–Hawking formula has been determined.     

Nonthermal effect of dilatonic black holes

The quantum nonthermal effect of the spherically symmetric and rotating dilatonic black holes is studied. A crossing of the positive and negative Dirac energy of particles occurs near dilatonic black holes. We find that the dilaton coupling parameter α affects the energy of spontaneous radiant particles. The energy of particles decreases when the coupling parameter α increases.     

Are black holes black?

This work presents a resolution of the causality paradox formulated by T. D. Lee in the theory of the Unruh effect and in the theory of black holes. The basis of the resolution is to take into account the transformation of a pure state into a mixed state in a measurement, which leads to a corresponding modification of the Bogolyubov transformations, so that black holes remain black.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 95–97, May, 1989.The author thanks N. Sh. Urusova for discussion of the work.