Black Hole Configurations Research Articles

Riemann–Cartan Gravity with Dynamical Signature

Model of Riemann–Cartan gravity with varying signature of metric is considered. The basic dynamical variables of the formalism are vierbein, spin connection, and an internal metric in the tangent space. The corresponding action contains new terms, which depend on these fields. In general case the signature of the metric is determined dynamically. The Minkowski signature is preferred dynamically because the configurations with the other signatures are dynamically suppressed. We also discuss briefly the motion of particles in the background of the modified black hole configuration, in which inside the horizon the signature is that of Euclidean space–time.

Impacts of Generalized Uncertainty Principle on the Black Hole Thermodynamics and Phase Transition in a Cavity

In this work, we conduct a study regarding the thermodynamic evolution and the phase transition of a black hole in a finite spherical cavity subject to the generalized uncertainty principle. The results demonstrate that both the positive and negative generalized uncertainty principle parameters β0 can significantly affect the thermodynamic quantities, stability, critical behavior, and phase transition of the black hole. For β0 > 0, the black hole forms a remnant with finite temperature, finite mass, and zero local heat capacity in the last stages of evolution, which can be regarded as an elementary particle. Meanwhile, it undergoes one second-order phase transition and two Hawking-Page-type phase transitions. The Gross-Perry-Yaffe phase transition occurs for both large black hole configuration and small black hole configuration. For β0 < 0, the Gross-Perry-Yaffe phase transition occurs only for large black hole configuration, and the temperature and heat capacity of the black hole remnant is finite, whereas its mass is zero. This indicates the remnant is metastable and would be in the Hawking-Page-type phase transition forever. Specifically, according to the viewpoint of corpuscular gravity, the remnant can be interpreted as an additional metastable tiny black hole configuration, which never appears in the original case and the positive correction case.

Plebański-Demiański solutions with dynamical torsion and nonmetricity fields

We construct Plebański-Demiański stationary and axisymmetric solutions with two expanding and double principal null directions in the framework of Metric-Affine gauge theory of gravity. Starting from the new improved form of the metric with vanishing cosmological constant recently achieved by Podolský and Vrátný, we extend this form in the presence of a cosmological constant and derive the conditions under which the physical sources of the torsion and nonmetricity tensors provide dynamical contributions preserving it in Weyl-Cartan geometry. The resulting black hole configurations are characterised by the mass, orbital angular momentum, acceleration, NUT parameter, cosmological constant and electromagnetic charges of the Riemannian sector of the theory, as well as by the spin and dilation charges of the torsion and nonmetricity fields. The former is subject to a constraint representing a decoupling limit with the parameters responsible of axial symmetry, beyond which the geometry of the space-time is expected to be corrected.

Infinitesimally thin static scalar shells surrounding charged Gauss-Bonnet black holes

We reveal the existence of a new form of spontaneously scalarized black-hole configurations. In particular, it is proved that Reissner-Nordström black holes in the highly charged regime Q/M > (Q/M)crit = sqrt{21}/5 can support thin matter shells that are made of massive scalar fields with a non-minimal coupling to the Gauss-Bonnet invariant of the curved spacetime. These static scalar shells, which become infinitesimally thin in the dimensionless large-mass Mμ » 1 regime, hover a finite proper distance above the black-hole horizon [here {M, Q} are respectively the mass and electric charge of the central supporting black hole, and μ is the proper mass of the supported scalar field]. In addition, we derive a remarkably compact analytical formula for the discrete resonance spectrum {left{eta left(Q/M, Mmu; nright)right}}_{n=0}^{n=infty } of the non-trivial coupling parameter which characterizes the bound-state charged-black-hole-thin-massive-scalar-shell cloudy configurations of the composed Einstein-Maxwell-scalar field theory.

Black hole thermodynamics is extensive with variable Newton constant

Inspired by the recent studies on the thermodynamics of AdS black holes in the restricted phase space formalism, we propose a similar formalism for the thermodynamics of non-AdS black holes with variable Newton constant. It is shown that, by introducing the new variables N,μ, where N is proportional to the inverse Newton constant and μ its conjugate variable, referred to as the chemical potential, the black hole thermodynamics can be formulated in a form which is consistent with the standard extensive thermodynamics for open macroscopic systems, with the first law and the Euler relation hold simultaneously. This formalism has profound implications, in particular, the mass is a homogeneous function of the first order in the extensive variables and the intensive variables are zeroth order homogeneous functions. The chemical potential is shown to be closely related to the Euclidean action evaluated at the black hole configuration.

Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies

We investigate classical and quantum geometric information flow theories (respectively, GIFs and QGIFs) when the geometric flow evolution and field equations for nonholonomic Einstein systems, NES, are derived from Perelman-Lyapunov type entropic type functionals. In this work, the term NES encodes models of gravitational and matter fields interactions and their geometric flow evolution subjected to nonholonomic (equivalently, non-integrable, anholonomic) constraints. There are used canonical geometric variables which allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and (for self-similar geometric flows) Ricci soliton type configurations. Our approach is different from the methods and constructions elaborated for special classes of solutions characterized by area--hypersurface entropy, related holographic and dual gauge--gravity models, and conformal field theories, involving generalizations of the Bekenstein-Hawking entropy and black hole thermodynamics. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are analysed the most important properties (inequalities) for NES and defined and computed QGIF versions of the von Neumann, relative and conditional entropy; mutual information, (modified) entanglement and R\'{e}nyi entropy. We construct explicit examples of generic off-diagonal exact and parametric solutions describing stationary solitonic gravitational hierarchies and deformations of black hole configurations. Finally, we show how Perelman's entropy and geometric thermodynamic values, and extensions to GIF and QGIF models can be computed for various new classes of exact solutions which cannot be described following the Bekenstein-Hawking approach.

Planar black holes configurations and shear viscosity in arbitrary dimensions with shift and reflection symmetric scalar-tensor theories

In higher dimensions, we explore planar hairy black hole configurations for a special subclass of the Horndeski theory defined by two coupling functions depending on the kinetic term and enjoying shift symmetry and reflection symmetry. For this analysis, we derive a set of new solutions given by time-dependent as well as time-independent scalar field configurations. Additionally, we calculate their thermodynamic quantities by using Wald formalism satisfying the first law of thermodynamics as well as a Smarr relation. Together with the above, the Wald procedure allows us to compute the shear viscosity, showing that for a suitable choice of the coupling functions the Kovtun-Son-Starinets bound is violated.

Can We Prescribe the Physical Parameters of Multiple Black Holes?

The parabolic-hyperbolic form of the constraints and superposed Kerr-Schild black holes have already been used to provide a radically new initialization of binary black hole configurations. The method generalizes straightforwardly to multiple black hole systems. This paper is to verify that each of the global Arnowitt-Deser-Misner quantities of the constructed multiple black hole initial data can always be prescribed, as desired, in advance of solving the constraints. These global charges are shown to be uniquely determined by the physical parameters of the involved individual Kerr-Schild black holes.

Complexity conjecture of regular electric black holes

Recently, the action growth rate of a variety of four-dimensional regular magnetic black holes in F frame is obtained in [1]. Here, we study the action growth rate of a four-dimensional regular electric black hole in P frame that is the Legendre transformation of F frame. We also investigate the action growth rates of the Wheeler-De Witt patch for such black hole configurations at the late time and examine the Lloyd bound on the rate of quantum computation. We show that although the form of the Lloyd bound formula remains unaltered, the energy modifies due to a non-vanishing trace of the energy-momentum tensor and some extra terms may appear in the total growth action. We also investigate the asymptotic behavior of complexity in two conjectures for static and rotating regular black holes.

Black hole initial data by numerical integration of the parabolic–hyperbolic form of the constraints

The parabolic–hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is fourth-order accurate (in the spatial directions) while “time”-integration is made by using the method of lines with a fourth-order order accurate Runge–Kutta scheme. The proper implementation of the applied numerical method is verified by convergence tests and monitoring the relative and absolute errors is determined by comparing numerically and analytically known solutions of the constraints involving boosted and spinning vacuum single black hole configurations. The main part of our investigations is, however, centered on the construction of initial data for distorted black holes which, in certain cases, have non-negligible gravitational wave content. Remarkably, the applied new method is unprecedented in that it allows to construct initial data for highly boosted and spinning black holes, essentially for the full physical allowed ranges of these parameters. In addition, the use of the evolutionary form of the constraints is free from applying any sort of boundary conditions in the strong field regime.

Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island

The island rule for the entanglement entropy is applied to an eternal Reissner–Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.

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.

Isolation of flexural waves in a wide and low frequency range using a phononic beam with acoustic black hole configuration

We propose a phononic beam to realize flexural wave bandgaps in wide and low frequency regimes. A unit cell of the phononic beam consists of two uniform parts and a tapered part with acoustic black hole configuration sandwiched between uniform parts. We identify the effects of geometrical parameters of the ABH-based phononic beam on band structures and determine those geometrical parameters to obtain a bandgap from 3.6 Hz to 237.9 Hz with a lattice constant of 1/33 wavelength. For experimental realization, the displacement transmission of the phononic beam is measured by impact hammer test, and the result shows that low transmission of –35 dB to i–10 dB could be achieved in the wide bandgap.

Geometrothermodynamics of black holes with a nonlinear source

We study thermodynamics and geometrothermodynamics of a particular black hole configuration with a nonlinear source. We use the mass as fundamental equation, from which it follows that the curvature radius must be considered as a thermodynamic variable, leading to an extended equilibrium space. Using the formalism of geometrothermodynamics, we show that the geometric properties of the thermodynamic equilibrium space can be used to obtain information about thermodynamic interaction, critical points and phase transitions. We show that these results are compatible with the results obtained from classical black hole thermodynamics.

Scalarization-like mechanism through spacetime anisotropic scaling symmetry

We present a new family of exact black hole configurations, which is a solution to a generalized Einstein-Maxwell-Dilaton setup in arbitrary dimension. These solutions are asymptotically Lifshitz for any dynamical critical exponent $z\ensuremath{\ge}1$. It turns out that the existence of a nontrivial scalar field is a direct consequence of breaking the spacetime isotropic scaling symmetry. This black hole family accepts various interesting limits that link it to well-known solutions in both the isotropic and anisotropic cases. We study the thermodynamics of these field configurations showing that the first law is satisfied and providing the corresponding Smarr formula, both of these relations account for an electric contribution. Furthermore, we show that for a certain parameter region, the anisotropic field configuration with a nonzero scalar field is thermodynamically preferred. This observation, together with a direct verification of the so-called scalarization conditions, suggest that the emergence of the dilaton field is due to a mechanism similar to spontaneous scalarization.

The quantum mass gap of extremal black holes

Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a finite mass gap above the corresponding zero-temperature (extremal) black-hole configuration. In the present compact paper we explicitly prove that the minimum energy gap Egap=ħ2/M3, which characterizes the mass spectra of near-extremal charged Reissner-Nordström black holes, can be inferred from a simple semi-classical analysis.

Thermodynamics and geometrothermodynamics of Reissner-Nordström black holes in multidimensional power-law models

This article analyzes the geometric properties of the equilibrium variety of black holes on the background of a higher-dimensional model. Models with power-law dependence of multidimensional black hole models are considered as a special case. This work provides a general overview of the work on this topic. The main components of the formalism of geometric thermodynamics are considered and thermodynamics for this metric is presented, which is used here to analyze the equilibrium variety of configurations of black holes. The main part of this study is the consideration of a particular case for the study of thermodynamics and geometrothermodynamics of the Reissner-Nordstrom five-dimensional black hole in a gravitational field. For the five-dimensional Reissner-Nordström black hole, singularity points are determined at which second-order phase transitions occur, which show interactions in a gravitational field. It is shown that the manifestation of the curvature of the considered black hole with phase transitions occurring in it demonstrates its behavior in a gravitational field. It should be noted that the structure of the phase transition of a black hole may depend on the chosen model of the ensemble. Consequently, the only features in all considered scalar versions of curvature in the representation of entropy, mass and enthalpy, depending on thermodynamic parameters, arise from beyond the limits of applicability of the thermodynamic approach to a black hole, where it is assumed that it is impossible to apply the usual approaches of general relativity.

Thermodynamics of two aligned Kerr-Newman black holes

Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. Like in the electrostatic systems of two Reissner-Nordstr\"om black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $\ell$ turns out to be defined by the same simple formula $\ell=L\exp(\gamma_0)$, $L$ being the coordinate length of the strut and $\gamma_0$ the value of the metric function $\gamma$ on the strut, which permits the elaboration of $\ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.

General theory of large D membranes consistent with second law of thermodynamics

We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.

Horizons and the wave function of Planckian quantum black holes

At the Planck scale the distinction between elementary particles and black holes becomes fuzzy. The very definition of a “quantum black hole” (QBH) is an open issue. Starting from the idea that, at the Planck scale, the radius of the event horizon undergoes quantum oscillations, we introduce a black hole mass-radius Generalized Uncertainty Principle (GUP) and derive a corresponding gravitational wavelength. Next we recover a GUP encoding effective geometry. This semi-classical gravitational description admits black hole configurations only for masses higher than the Planck mass. Quantum corrections lead to a vanishing Hawking temperature when the Planck mass is approached from above. Finally we replace our semi-classical model by a relativistic wave equation for the “horizon wave function”. The solution admits a discrete mass spectrum which is bounded from below by a stable ground state with energy close to the Planck mass. Interestingly higher angular momentum states fit onto Regge trajectories indicating their stringy nature.