The mass of a Lifshitz black hole

It is well known that massive 3D gravity admits solutions that describe Lifshitz black holes as those considered in non-relativistic holography. However, the determination of the mass of such black holes remained unclear as many different results were reported in the literature presenting discrepancies. Here, by using a robust method that permits to tackle the problem in the strong field regime, we determine the correct mass of the Lifshitz black hole of the higher-derivative massive gravity and compare it with other results obtained by different methods. Positivity of the mass spectrum demands an odd normalization of the gravity action. In spite of this fact, the result turns out to be consistent with computations inspired in holography.

Holographic Lifshitz superconductors with Weyl correction

At the probe approximation, we construct a holographic p-wave conductor/superconductor model in the five-dimensional Lifshitz black hole with the Weyl correction via both numerical and analytical methods, and study the effects of the Lifshitz parameter z as well as the Weyl parameter $$\gamma $$ γ on the superconductor model. As we take into account one of the two corrections separately, the increasing z ($$\gamma $$ γ ) inhibits(enhances) the superconductor phase transition. When the two corrections are considered comprehensively, they display the obviously competitive effects on both the critical temperature and the vector condensate. In particular, the promoting effects of the Weyl parameter $$\gamma $$ γ on the critical temperature are obviously suppressed by the increasing Lifshitz parameter. Meanwhile, in the case of $$z<2.35$$ z < 2.35 ($$z>2.35$$ z > 2.35 ), the condensate at lower temperature decreases(increases) with the increasing Weyl parameter $$\gamma $$ γ . What is more, the difference among the condensate with the fixed Weyl parameter($$\gamma =-\frac{6}{100},0,\frac{4}{100}$$ γ = - 6 100 , 0 , 4 100 ) decreases(increases) with the increasing Lifshitz parameter z in the region $$z<2.35$$ z < 2.35 ($$z>2.35$$ z > 2.35 ). Furthermore, the increasing z obviously suppresses the real part of conductivity for all value of the Weyl parameter $$\gamma $$ γ . In addition, the analytical results agree well with the ones from the numerical method.

New version of the gedanken experiments to test the weak cosmic censorship in charged dilaton-Lifshitz black holes

In this paper, based on the new version of the gedanken experiments proposed by Sorce and Wald, we examine the weak cosmic censorship in the perturbation process of accreting matter fields for the charged dilaton-Lifshitz black holes. In the investigation, we assume that the black hole is perturbed by some extra matter source satisfied the null energy condition and ultimately settle down to a static charged dilaton-Lifshitz black hole in the asymptotic future. Then, after applying the Noether charge method, we derive the first-order and second-order perturbation inequalities of the perturbation matter fields. As a result, we find that the nearly extremal charged dilaton-Lifshitz black hole cannot be destroyed under the second-order approximation of perturbation. This result implies that the weak cosmic censorship conjecture might be a general feature of the Einstein gravity, and it is independent of the asymptotic behaviors of the black holes.

Fermion clouds around z = 0 Lifshitz black holes

In this work, the Dirac equation is studied in the [Formula: see text] Lifshitz black hole ([Formula: see text]LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod’s iteration method. Finally, Maggiore’s method (MM) is employed to derive the entropy/area spectra of the [Formula: see text]LBH which are shown to be equidistant.

Charged scalar quasi-normal modes for higher-dimensional Born–Infeld dilatonic black holes with Lifshitz scaling

We study quasi-normal modes for a higher dimensional black hole with Lifshitz scaling, as these quasi-normal modes can be used to test Lifshitz models with large extra dimensions. We analyze quasi-normal modes for higher dimensional dilaton-Lifshitz black hole solutions coupled to a non-linear Born–Infeld action. We will analyze the charged perturbations for such a black hole solution. We will first analyze the general conditions for stability analytically, for a positive potential. Then, we analyze this system for a charged perturbation as well as negative potential, using the asymptotic iteration method for quasi-normal modes.

The Lagrangian of charged test particle in Horava-Lifshitz black hole and deformed phase space

We use deformation approach and obtain Lagrangian of charged test particle. We show the effect of non-commutative parameters [Formula: see text] and [Formula: see text] on the Lagrangian of a test particle in Horava-Lifshitz background with charge and without charge and see in the case of [Formula: see text] and without charge, the deformed and non-deformed Lagrangian will be the same. In the case of [Formula: see text] and with charge will be the same but the charge or field need some scaling. Finally, results in the case of [Formula: see text] with charge are completely different. It means that we have other components in addition to having a time component of the field.

Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

In this paper we investigate the thermodynamic properties of the stationary Lifshitz black hole solution of New Massive Gravity. We study the thermodynamic stability from local and global point of view. We also consider the space of equilibrium states for the solution within the framework of thermodynamic information geometry. By investigating the proper thermodynamic metrics and their curvature invariants we find a set of restrictions on the parameter space and the critical points indicating phase transitions of the system. We confirm our findings by analytical analysis of the geodesics on the space of equilibrium states.