Lifshitz Black Hole Research Articles

Extended thermodynamics and critical behavior of generalized dilatonic Lifshitz black holes

We study a particular Einstein–Maxwell–Dilaton black hole configuration with cosmological constant, expressed in terms of the curvature radius, from the point of view of quasi-homogeneous thermodynamics. In particular, we show that the curvature radius and the coupling constant of the matter fields can be treated as thermodynamic variables in the framework of extended thermodynamics, leading in both cases to a van der Waals-like behavior. We also investigate in detail the stability and critical properties of the black holes and obtain results, which are compatible with the mean field approach.

Lyapunov exponents and phase structure of Lifshitz and hyperscaling violating black holes

We study the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. For describing hyperscaling violating system, we chose a particular gravity model constructed from generalized Einstein-Maxwell-Dilaton action which includes the Lifshitz cases at appropriate limits. We study the relationship between Lyapunov exponents and black hole phase transitions considering both the timelike and null geodesics. We observe that, the black hole phase transiton properties are reflected in Lyapunov exponent where its multiple branches correspond to the distinct phases of the black hole. The discontinuos change of the Lyapunov exponent during the phase transition serve as an order parameter with critical exponent 1/2 near the critical point. Our numerical study reveals that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalised beyond the AdS spacetime. We find that it is independent of the HSV parameter as well as the Lifshitz exponent.

Regularized Weyl double copy

We propose a regularization procedure in the sourced Weyl double copy, a spinorial version of the classical double copy, such that it matches much more general results in the Kerr-Schild version. In the regularized Weyl double copy, the anti–de Sitter (AdS) and the Lifshitz black holes, which form the basis of the study of strongly coupled gauge theories at finite temperature through the AdS/CFT correspondence and its nonrelativistic generalization, become treatable. We believe that this might pave the way for finding a relation between the classical double copy and holography. Published by the American Physical Society 2024

Einstein–Bumblebee-dilaton black hole in Lifshitz spacetimes

We investigate the critical behavior of Lifshitz black holes in Einstein-dilaton gravity in the context of spontaneous Lorentz symmetry breaking. Considering the effects of both the Bumblebee vacuum expectation value (VEV) and the fluctuations over the VEV, we obtained new asymptotically Lifshitz charged solutions in (3 + 1) dimensions. We consider the longitudinal massive mode of Lorentz violation (LV) as thermodynamic pressure, leading us to establish an P-V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P-V$$\\end{document} extended phase space. Within this framework, we derive the equation of state P(T, V), and subsequently identify the critical points, which manifest as discontinuities in the specific heat at constant pressure. Following this, we compute the Gibbs free energy, revealing a first-order phase transition within the model. Finally, we determine the critical exponents, demonstrating their equivalence to those observed in the Van der Waals system.

Topology of Hořava–Lifshitz black holes in different ensembles

In this paper, we study topological numbers for uncharged and charged static black holes obtained in z=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=3$$\\end{document} Hořava–Lifshitz gravity theory in different ensembles, where z measures the degree of anisotropy between space and time. We first calculate the topological numbers for the uncharged black holes by changing the value of the dynamic coupling constant, and find that the black holes with spherical and flat horizons have the same topological number. When the black hole’s horizon is hyperbolic, different values of the coupling constant generate different topological numbers, which can be 1, 0 or -1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-1$$\\end{document}. This shows that the coupling constant plays an important role in the topological classification. Then we study the topological numbers for the charged black holes in different ensembles. The black hole with a spherical horizon has the same topological number in canonical and grand canonical ensembles. When the horizons are flat or hyperbolic, they have different topological numbers in canonical and grand canonical ensembles. Therefore, the topological numbers for the uncharged black holes are parameter dependent, and those for the charged black holes are ensemble dependent.

Charged Lifshitz black holes from general covariance breaking

In this work we use a general covariance breaking mechanism to obtain a class of charged black holes whose background geometry asymptotically approaches Lifshitz spacetimes. We discuss how this method affects Einstein’s equations and explore the thermodynamics and critical behavior of the solution found.

A zoo of deformed Jackiw-Teitelboim models near large dimensional black holes

We consider a charged Lifshitz black hole in the large transverse dimension limit. In this setup, the dynamics near the black hole horizon are shown to be effectively governed by a family of two-dimensional models of dilaton gravity depending on the ratio of the dynamical parameter characterizing the black hole and the dimension of spacetime. This family includes the Callan-Giddings-Harvey-Strominger (CGHS) and Jackiw-Teitelboim (JT) models and their charged equivalents. This family also contains classes of asymptotically anti-de Sitter models beyond JT, characterized by a running Ricci scalar, with the option of adding charge. Finally, we argue that specific non-minimally coupled probe scalars in the parent Lifshitz model become minimally coupled scalars in the two-dimensional theory, which is relevant for understanding semi-classical corrections in such models.

Scalar fields and Lifshitz black holes from Derrick’s theorem evasion

We study classical scalar fields in asymptotically Lifshitz spacetimes. By evading Derrick's theorem requiring the scalar potential to explicitly depend on the background coordinates, we induce a diffeomorphism invariance breaking and settle a formalism to find spatially localized solutions in the probe field limit. By inserting a backreaction equipped with a cosmological constant and a Maxwell term coupled to a dielectric function in the model, we find a Lifshitz black hole solution.

Non-perturbative correction to the Hořava–Lifshitz black hole thermodynamics

In this paper, we consider non-perturbative quantum correction which appears as exponential term in the black hole entropy. We study consequence thermodynamics of the Ho\v{r}ava-Lifshitz black hole at quantum scales. We consider two cases of Kehagius-Sfetsos and Lu-Mei-Pop solutions and investigate black hole stability. We find that non-perturbative quantum correction yields to an instability at infinitesimal horizon radius of Kehagius-Sfetsos solution. On the other hand, non-perturbative quantum correction yields to the stability of Lu-Mei-Pop solution. Hence, we find that holographic dual of Lu-Mei-Pop black hole (in absence of non-perturbative quantum correction) is the interacting gas of point like particles, while it is Van der Waals fluid in presence of non-perturbative quantum correction.

Lifshitz scaling effects on the holographic model for paramagnetism-antiferromagnetism phase transition

In this work, we construct a holographic antiferromagnetism model by introducing two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other in the four-dimensional Lifshitz black hole, and investigate the effects of Lifshitz dynamical exponent z on the paramagnetism-antiferromagnetism phase transition in detail. Using the numerical shooting method, we find that there is still a phase transition in asymptotically Lifshitz space-time in the probe limit. In the absence of an external magnetic field and in low temperature, the magnetic moments condense spontaneously in antiparallel manner with the same magnitude. But the critical temperature and the staggered magnetization decrease with increasing z, which makes paramagnetism-antiferromagnetism phase transition harder to happen. In the presence of the weak external magnetic field, the magnetic susceptibility has a peak at the critical temperature and increasing values of z makes the peak higher. In the case of the strong external magnetic field, there exists a critical magnetic field Bc in the antiferromagnetic phase. When the magnetic field reaches Bc, the system turns into the paramagnetic phase. Besides, the increasing of z results in increasing of Bc.

Lifshitz black holes in four-dimensional critical gravity

In this work, we study the existence of asymptotically Lifshitz black holes in Critical Gravity in four dimensions with a negative cosmological constant under two scenarios: First, including dilatonic fields as the matter source, where we find an asymptotically Lifshitz solution for a fixed value of the dynamical exponent $z=4$. As a second case, we also added a non-minimally coupled scalar field $\Phi$ with a potential given by a mass term and a quartic term. Using this approach, we found a solution for $z$ defined in the interval $(1,4)$, recovering the Schwarzchild-Anti-de Sitter case with planar base manifold in the isotropic limit. Moreover, when we analyzed the limiting case $z=4$, we found that there exists an additional solution that can be interpreted as a stealth configuration in which the stealth field is overflying the $z=4$ solution without the non-minimally coupled field $\Phi$. Finally, we studied the non-trivial thermodynamics of these new anisotropic solutions and found that they all satisfy the First Law of Thermodynamics as well as the Smarr relation. We were also able to determine that the non-stealth configuration is thermodynamically preferred in this case.

Holographic stress tensor of colored Lifshitz spacetimes and hairy black holes

We compute the holographic stress tensor of colored Lifshitz spacetimes following the proposal by Ross-Saremi for gravity duals of non-relativistic theories. For a well-defined variational principle, we first construct a finite on-shell action for the Einstein-Yang-Mills model in four dimensions with Lifshitz spacetime as a solution. We then solve the linearised equations of motion and identify the modes that preserve the asymptotically Lifshitz condition. Employing these modes, we also show that the stress tensor is finite, obeying the scaling and the diffeomorphism Ward identities, i.e., conservations laws. As a final application, we evaluate the energy density and the spatial stress tensor of the previously found numerical black hole solutions with various dynamical exponents z. The alternative Smarr relation that has been used in Lifshitz black holes and the first law of thermodynamics are shown to hold without a global Yang-Mills charge, indicating the black holes in question are hairy.

Rotating spacetimes generalizing Lifshitz black holes

We present a spinning black hole solution in d dimensions with a maximal number of rotation parameters in the context of the Einstein–Maxwell-Dilaton theory. An interesting feature of such a solution is that it accommodates Lifshitz black holes when the rotation parameters are set to zero. We verify the rotating nature of the black hole solution by performing the quasi-local analysis of conserved charges and defining the corresponding angular momenta. In addition, we perform the thermodynamical analysis of the black hole configuration, show that the first law of thermodynamics is completely consistent, and obtain a Smarr-like formula. We further study the thermodynamic stability of the constructed solution from a local viewpoint, by computing the associated specific heats, and from a global perspective, by using the so-called new thermodynamic geometry. We finally make some comments related to a pathology found in the causal structure of the obtained rotating black hole spacetime and compute some of its curvature invariants.

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.

Exact solutions of Lifshitz black hole coupled with nonlinear electrodynamics Journal of Physics: Conference Series

In the paper, we find an exact black hole solution in Lifshitz space time coupled with nonlinear electrodynamics and investigate their thermodynamic quantities connected with the black hole in term of horizon radius. This black hole solution interpolates with the Lifshitz black hole in the absence of magnetic monopole charge and Bardeen black hole when z = 0.

The Kerr-Schild double copy in Lifshitz spacetime

The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

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 on the superconductor model. As we take into account one of the two corrections separately, the increasing z (gamma ) 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 on the critical temperature are obviously suppressed by the increasing Lifshitz parameter. Meanwhile, in the case of z<2.35(z>2.35), the condensate at lower temperature decreases(increases) with the increasing Weyl parameter gamma . What is more, the difference among the condensate with the fixed Weyl parameter(gamma =-frac{6}{100},0,frac{4}{100}) decreases(increases) with the increasing Lifshitz parameter z in the region 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 . In addition, the analytical results agree well with the ones from the numerical method.

Holographic complexity for nonlinearly charged Lifshitz black holes

Using ‘complexity = action’ proposal we study the late time growth rate of holographic complexity for nonlinear charged Lifshitz black hole with a single horizon or two horizons. As a toy model, we consider two kinds of such black holes: nonlinear charged Lifshitz black hole and nonlinear logarithmic charged Lifshitz black hole. We find that for the black hole with two horizons, the action growth bound is satisfied. But for the black hole with a single horizon, whether the Lloyd bound is violated depends on the specific value of dimensionless coupling constants β 1, β 2, spacetime dimension D and dynamical exponent z.

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.

Holographic information theoretic quantities for Lifshitz black hole

In this paper, we have investigated the holographic entanglement entropy for a linear subsystem in a 3+1-dimensional Lifshitz black hole. The entanglement entropy has been analysed in both the infra-red and ultra-violet limits, and has also been computed in the near horizon approximation. The notion of a generalized temperature in terms of the renormalized entanglement entropy has been introduced. This also leads to a generalized thermodynamics like law E=frac{1}{2}T_g S_{REE}. The generalized temperature has been defined in such a way that it reduces to the Hawking temperature in the infra-red limit. We find that the inverse of the generalized temperature (beta _g=1/T_g) attains a non-zero value when the subsystem length becomes zero although it is zero in case of the Schwarzschild-AdS black hole. We have then computed the holographic subregion complexity. We find that the subregion complexity has logarithmic divergence which was absent in case of the 3+1-dimensional Schwarzschild-AdS black hole. Then the Fisher information metric and the fidelity susceptibility for the same linear subsystem have also been computed using the bulk dual prescriptions. It has been observed that the two metrics are not related to each other.