Topological Black Hole Solutions Research Articles

Thermodynamic Topology of Topological Black Hole in F(R)-ModMax Gravity’s Rainbow

Abstract In order to include the effect of high energy and topological parameters on black holes in $\mathrm{ F}(R)$ gravity, we consider two corrections to this gravity: energy-dependent spacetime with different topological constants, and a nonlinear electrodynamics field. In other words, we combine $\mathrm{ F}(R)$ gravity’s rainbow with ModMax nonlinear electrodynamics theory to see the effects of high energy and topological parameters on the physics of black holes. For this purpose, we first extract topological black hole solutions in $\mathrm{ F}(R)$-ModMax gravity’s rainbow. Then, by considering black holes as thermodynamic systems, we obtain thermodynamic quantities and check the first law of thermodynamics. The effect of the topological parameter on the Hawking temperature and the total mass of black holes is obvious. We also discuss the thermodynamic topology of topological black holes in $\mathrm{ F}(R)$-ModMax gravity’s rainbow using the off-shell free energy method. In this formalism, black holes are assumed to be equivalent to defects in their thermodynamic spaces. For our analysis, we consider two different types of thermodynamic ensembles. These are: fixed q ensemble and fixed $\phi$ ensemble. We take into account all the different types of curvature hypersurfaces that can be constructed in these black holes. The local and global topology of these black holes are studied by computing the topological charges at the defects in their thermodynamic spaces. Finally, in accordance with their topological charges, we classify the black holes into three topological classes with total winding numbers corresponding to $-1, 0$, and 1. We observe that the topological classes of these black holes are dependent on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles.

Conformal Renormalization of topological black holes in AdS6

We present a streamlined proof that any Einstein-AdS space is a solution of the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction of conformal gravity into Einstein theory manifestly shows that the action of the latter can be written as the Einstein-Hilbert term plus the Euler topological density and an additional contribution that depends on the Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this form of the action by embedding the Einstein theory into a Weyl-invariant purely metric theory, was dubbed Conformal Renormalization and its resulting action was shown to be equivalent to the one obtained by holographic renormalization. As a non-trivial application of the method, we compute the Noether-Wald charges and thermodynamic quantities for topological black hole solutions with generic transverse section in Einstein-AdS6 theory.

Analytic topological hairy dyonic black holes and thermodynamics

We present and discuss a new family of topological hairy dyonic black hole solutions in asymptotically anti--de Sitter space. The coupled Einstein-Maxwell-scalar gravity system, that carries both the electric and magnetic charges is solved, and exact hairy dyonic black hole solutions are obtained analytically. The scalar field profiles that give rise to such black hole solutions are regular everywhere. The hairy solutions are obtained for planar, spherical, and hyperbolic horizon topologies. In addition, analytic expressions of regularized action, stress tensor, conserved charges, and free energies are obtained. We further comment on different prescriptions for computing the black hole mass with hairy backgrounds. We analyze the thermodynamics of these hairy dyonic black holes in canonical and grand canonical ensembles, and we find that both electric and magnetic charges have a constructive effect on the stability of the hairy solution. For the case of planar and hyperbolic horizons, we find thermodynamically stable hairy black holes that are favored at low temperatures compared to the nonhairy counterparts. We further find that, for a spherical hairy dyonic black hole, the thermodynamic phase diagram resembles to that of a Van der Waals fluid not only in canonical but also in the grand canonical ensemble.

Spatially homogeneous black hole solutions in z=4 Ho\u0159ava\u2013Lifshitz gravity in (4+1) dimensions with Nil geometry and H^2times R horizons

In this paper, we present two new families of spatially homogeneous black hole solution for z=4 Hořava–Lifshitz Gravity equations in (4+1) dimensions with general coupling constant lambda and the especial case lambda =1, considering beta =-1/3. The three-dimensional horizons are considered to have Bianchi types II and III symmetries, and hence the horizons are modeled on two types of Thurston 3-geometries, namely the Nil geometry and H^2times R. Being foliated by compact 3-manifolds, the horizons are neither spherical, hyperbolic, nor toroidal, and therefore are not of the previously studied topological black hole solutions in Hořava–Lifshitz gravity. Using the Hamiltonian formalism, we establish the conventional thermodynamics of the solutions defining the mass and entropy of the black hole solutions for several classes of solutions. It turned out that for both horizon geometries the area term in the entropy receives two non-logarithmic negative corrections proportional to Hořava–Lifshitz parameters. Also, we show that choosing some proper set of parameters the solutions can exhibit locally stable or unstable behavior.

Topological black holes in mimetic gravity

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space–time. (ii) We also investigate the casual structure and physical properties of the solutions. We observe that in the absence of a potential, our solutions are not asymptotically flat, while in the presence of a negative constant potential for the mimetic field, the solutions are asymptotically anti-de Sitter (AdS). (iii) Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.

Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity

We investigate a new class of [Formula: see text]-dimensional topological black hole solutions in the context of massive gravity and in the presence of logarithmic nonlinear electrodynamics. Exploring higher-dimensional solutions in massive gravity coupled to nonlinear electrodynamics is motivated by holographic hypothesis as well as string theory. We first construct exact solutions of the field equations and then explore the behavior of the metric functions for different values of the model parameters. We observe that our black holes admit the multi-horizons caused by a quantum effect called anti-evaporation. Next, by calculating the conserved and thermodynamic quantities, we obtain a generalized Smarr formula. We find that the first law of black holes thermodynamics is satisfied on the black hole horizon. We study thermal stability of the obtained solutions in both canonical and grand canonical ensembles. We reveal that depending on the model parameters, our solutions exhibit a rich variety of phase structures. Finally, we explore, for the first time without extending thermodynamics phase space, the critical behavior and reentrant phase transition for black hole solutions in massive gravity theory. We realize that there is a zeroth-order phase transition for a specified range of charge value and the system experiences a large/small/large reentrant phase transition due to the presence of nonlinear electrodynamics.

Topological Born\u2013Infeld charged black holes in Einsteinian cubic gravity

In this paper, we study four-dimensional topological black hole solutions of Einsteinian cubic gravity in the presence of nonlinear Born–Infeld electrodynamics and a bare cosmological constant. First, we obtain the field equations which govern our solutions. Employing Abbott–Deser–Tekin and Gauss formulas, we present the expressions of conserved quantities, namely total mass and total charge of our topological black solutions. We disclose the conditions under which the model is unitary and perturbatively free of ghosts with asymptotically (A)dS and flat solutions. We find that, for vanishing bare cosmological constant, the model is unitary just for asymptotically flat solutions, which only allow horizons with spherical topology. We compute the temperature for these solutions and show that it always has a maximum value, which decreases as the values of charge, nonlinear coupling or cubic coupling grows. Next, we calculate the entropy and electric potential. We show that the first law of thermodynamics is satisfied for spherical asymptotically flat solutions. Finally, we peruse the effects of model parameters on thermal stability of these solutions in both canonical and grand canonical ensembles.

Exact topological charged hairy black holes in AdS space in d dimensions

We present a new family of topological charged hairy black hole solutions in asymptotically AdS space in $D$-dimensions. We solve the coupled Einstein-Maxwell-Scalar gravity system and obtain exact charged hairy black hole solutions with planar, spherical and hyperbolic horizon topologies. The scalar field is regular everywhere. We discuss the thermodynamics of the hairy black hole and find drastic changes in its thermodynamic structure due to the scalar field. For the case of planar and spherical horizons, we find charged hairy/RN-AdS black hole phase transition, with thermodynamically preferred and stable charged hairy phases at low temperature. For the case of hyperbolic horizon, no such transition occurs and RN-AdS black holes are always thermodynamically favoured.

Quadratic gravity and conformally coupled scalar fields

We construct black hole solutions in four-dimensional quadratic gravity, supported by a scalar field conformally coupled to quadratic terms in the curvature. The conformal matter Lagrangian is constructed with powers of traces of a conformally covariant tensor, which is defined in terms of the metric and a scalar field, and has the symmetries of the Riemann tensor. We find exact, neutral and charged, topological black hole solutions of this theory when the Weyl squared term is absent from the action functional. Including terms beyond quadratic order on the conformally covariant tensor, allows to have asymptotically de Sitter solutions, with a potential that is bounded from below. For generic values of the couplings we also show that static black hole solutions must have a constant Ricci scalar, and provide an analysis of the possible asymptotic behavior of both, the metric as well as the scalar field in the asymptotically AdS case, when the solutions match those of general relativity in vacuum at infinity. In this frame, the spacetime fulfils standard asymptotically AdS boundary conditions, and in spite of the non-standard couplings between the curvature and the scalar field, there is a family of black hole solutions in AdS that can be interpreted as localized objects. We also provide further comments on the extension of these results to higher dimensions.

New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory

We construct black hole solutions to the leading order of string effective action in five dimensions with the source given by dilaton and magnetically charged antisymmetric gauge B-field. Presence of the considered B-field leads to the unusual asymptotic behavior of the solutions which are neither asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional space part to correspond to the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston’s geometries of E^3, S^3, H^3, H^2 times E^1, widetilde{{SL_2R}}, nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature, entropy, dilaton charge, and magnetic potential, we show that the first law of black hole thermodynamics is satisfied by these quantities and the dilaton charge is not independent of mass and magnetic charge. Furthermore, for Bianchi type V, the T-dual black hole solution is obtained which carries no charge associated with B-field and the entropy turns to be invariant under the T-duality.

Magnetized topological black holes of dimensionally continued gravity

In this paper, a large family of topological black hole solutions of dimensionally continued gravity are derived. The action of Lovelock gravity is coupled to the exponential electrodynamics and the equations of motion are solved in the presence of a pure magnetic source. We work out the metric functions in terms of the parameter $\beta$ of exponential electrodynamics, and magnetic charge. Further, we couple Lovelock gravity to power-Yang-Mills theory and construct black holes, in diverse dimensions, having Yang-Mills magnetic charge. We also discuss the asymptotic bahaviour of metric functions and curvature invariants at the origin for both the models. The thermodynamics of resulting magnetized black hole solutions in the framework of two different models is also studied. The thermodynamical quantities like Hawking temperature, entropy and specific heat capacity at constant charge are found and we show that the resulting quantities satisfy the first law of black hole thermodynamics. We also study the magnetized hairy black holes of dimensionally continued gravity.

Thermal stability of a special class of black hole solutions in F(R) gravity

In this paper, we work on the topological Lifshitz-like black hole solutions of a special class of vacuum F(R)-gravity that are static and spherically symmetric. We investigate geometric and thermodynamic properties of the solutions with due respect to the validity of the first law of thermodynamics. We examine the van der Waals like behavior for asymptotically AdS solutions with spherical horizon by studying the P-v, G-T and C_{Q,P}-r_{+} diagrams and find a consistent result. We also investigate the same behavior for hyperbolic horizon and interestingly find that the system under study can experience a phase transition with negative temperature.

Criticality and extended phase space thermodynamics of AdS black holes in higher curvature massive gravity

Considering de Rham–Gabadadze–Tolley theory of massive gravity coupled with (ghost free) higher curvature terms arisen from the Lovelock Lagrangian, we obtain charged-AdS black hole solutions in diverse dimensions. We compute thermodynamic quantities in the extended phase space by considering the variations of the negative cosmological constant, Lovelock coefficients (alpha _{i}) and massive couplings (c_{i}). We also prove that such variations are necessary in order to satisfy the extended first law of thermodynamics as well as associated Smarr formula. In addition, by performing a comprehensive thermal stability analysis for the topological black hole solutions, we show that in which regions thermally stable phases exist. Calculations show the results are radically different from those in the Einstein gravity. We find that the phase structure and critical behavior of topological AdS black holes are drastically restricted by the geometry of the event horizon. We also show that the phase structure of AdS black holes with non-compact (hyperbolic) horizon could give birth to three critical points corresponds to a reverse van der Waals behavior for phase transition which is accompanied with two distinct van der Waals phase transitions. For black holes with the spherical horizon, the van der Waals, reentrant and analogue of solid/liquid/gas phase transitions are observed.

Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics

We obtain topological black hole solutions in scalar-tensor gravity with nonminimal derivative coupling between scalar and tensor components of gravity and power-law Maxwell field minimally coupled to gravity. The obtained solutions can be treated as a generalization of previously derived charged solutions with standard Maxwell action \cite{Feng_PRD16}. We examine the behaviour of obtained metric functions for some asymptotic values of distance and coupling. To obtain information about singularities of the metrics we calculate Kretschmann scalar. We also examine the behaviour of gauge potential and show that it is necessary to impose some constraints on parameter of nonlinearity in order to obtain reasonable behaviour of the filed. The next part of our work is devoted to the examination of black hole's thermodynamics. Namely we obtain black hole's temperature and investigate it in general as well as in some particular cases. To introduce entropy we use well known Wald procedure which can be applied to quite general diffeomorphism-invariant theories. We also extend thermodynamic phase space by introducing thermodynamic pressure related to cosmological constant and as a result we derive generalized first law and Smarr relation. The extended thermodynamic variables also allow us to construct Gibbs free energy and its examination gives important information about thermodynamic stability and phase transitions. We also calculate heat capacity of the black holes which demonstrates variety of behaviour for different values of allowed parameters.

Holographic conductivity in the massive gravity with power-law Maxwell field

We obtain a new class of topological black hole solutions in (n+1)-dimensional massive gravity in the presence of the power-Maxwell electrodynamics. We calculate the conserved and thermodynamic quantities of the system and show that the first law of thermodynamics is satisfied on the horizon. Then, we investigate the holographic conductivity for the four and five dimensional black brane solutions. For completeness, we study the holographic conductivity for both massless (m=0) and massive (m≠0) gravities with power-Maxwell field. The massless gravity enjoys translational symmetry whereas the massive gravity violates it. For massless gravity, we observe that the real part of conductivity, Re[σ], decreases as charge q increases when frequency ω tends to zero, while the imaginary part of conductivity, Im[σ], diverges as ω→0. For the massive gravity, we find that Im[σ] is zero at ω=0 and becomes larger as q increases (temperature decreases), which is in contrast to the massless gravity. It also has a maximum value for ω≠0 which increases with increasing q (with fixed p) or increasing p (with fixed q) for (2+1)-dimensional dual system, where p is the power parameter of the power-law Maxwell field. Interestingly, we observe that in contrast to the massless case, Re[σ] has a maximum value at ω=0 (known as the Drude peak) for p=(n+1)/4 (conformally invariant electrodynamics) and this maximum increases with increasing q. In this case (m≠0) and for different values of p, the real and imaginary parts of the conductivity has a relative extremum for ω≠0. Finally, we show that for high frequencies, the real part of the holographic conductivity have the power law behavior in terms of frequency, ωa where a∝(n+1−4p). Some similar behaviors for high frequencies in possible dual CFT systems have been reported in experimental observations.

Black hole thermodynamics in Lovelock gravity's rainbow with (A)dS asymptote

In this paper, we combine Lovelock gravity with gravity's rainbow to construct Lovelock gravity's rainbow. Considering the Lovelock gravity's rainbow coupled to linear and also nonlinear electromagnetic gauge fields, we present two new classes of topological black hole solutions. We compute conserved and thermodynamic quantities of these black holes (such as temperature, entropy, electric potential, charge and mass) and show that these quantities satisfy the first law of thermodynamics. In order to study the thermal stability in canonical ensemble, we calculate the heat capacity and determinant of the Hessian matrix and show in what regions there are thermally stable phases for black holes. Also, we discuss the dependence of thermodynamic behavior and thermal stability of black holes on rainbow functions. Finally, we investigate the critical behavior of black holes in the extended phase space and study their interesting properties.

Topological black holes in [formula omitted] Einstein–Yang–Mills theory with a negative cosmological constant

We investigate the phase space of topological black hole solutions of su(N) Einstein–Yang–Mills theory in anti-de Sitter space with a purely magnetic gauge potential. The gauge field is described by N−1 magnetic gauge field functions ωj, j=1,…,N−1. For su(2) gauge group, the function ω1 has no zeros. This is no longer the case when we consider a larger gauge group. The phase space of topological black holes is considerably simpler than for the corresponding spherically symmetric black holes, but for N>2 and a flat event horizon, there exist solutions where at least one of the ωj functions has one or more zeros. For most of the solutions, all the ωj functions have no zeros, and at least some of these are linearly stable.

Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field

In this paper, we present a new class of higher dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon.

Phase transition and thermodynamic geometry of topological dilaton black holes in gravitating logarithmic nonlinear electrodynamics

Considering the Lagrangian of the logarithmic nonlinear electrodynamics in the presence of a scalar dilaton field, we obtain a new class of topological black hole solutions of Einstein-dilaton gravity with two Liouville-type dilaton potentials. Black hole horizons and cosmological horizons, in these spacetimes, can be a two-dimensional positive, zero, or negative constant curvature surface. We find that the behavior of the electric field crucially depends on the dilaton coupling constant $\ensuremath{\alpha}$. For small $\ensuremath{\alpha}$, the electric field diverges near the origin, although its divergency is weaker than the linear Maxwell field. However, with increasing $\ensuremath{\alpha}$, the behavior of the electric field, near the origin, approaches to that of the Maxwell field. We also study casual structure, asymptotic behavior, and physical properties of the solutions. We find that, depending on the model parameters, the topological dilaton black holes may have one or two horizons, and even in some cases we encounter a naked singularity without horizon. We compute the conserved and thermodynamic quantities of the spacetime and investigate that these quantities satisfy the first law of thermodynamics. We also probe thermal stability in the canonical and grand canonical ensembles and disclose the effects of the dilaton field as well as nonlinear parameter on the thermal stability of the solutions. Finally, we investigate thermodynamical geometry of the obtained solutions by introducing a new metric and studying the phase transition points due to the divergency of the Ricci scalar. We find that the dilaton field affects the phase transition points of the system.

Thermodynamics of topological black holes inR2gravity

We study topological black hole solutions of the simplest quadratic gravity action and we find that two classes are allowed. The first is asymptotically flat and mimics the Reissner-Nordstr\"om solution, while the second is asymptotically de Sitter or anti-de Sitter. In both classes, the geometry of the horizon can be spherical, toroidal or hyperbolic. We focus in particular on the thermodynamical properties of the asymptotically anti-de Sitter solutions and we compute the entropy and the internal energy with Euclidean methods. We find that the entropy is positive-definite for all horizon geometries and this allows to formulate a consistent generalized first law of black hole thermodynamics, which keeps in account the presence of two arbitrary parameters in the solution. The two-dimensional thermodynamical state space is fully characterized by the underlying scale invariance of the action and it has the structure of a projective space. We find a kind of duality between black holes and other objects with the same entropy in the state space. We briefly discuss the extension of our results to more general quadratic actions.