Exact Black Hole Research Articles

On black holes with scalar hairs

By using the Taylor series and the solution-generating methods, we construct exact black hole solutions with minimally coupled scalar fields. We find that the black hole solutions can have many hairs except for the physical mass. These hairs come from the scalar potential. Different from the mass, there is no symmetry corresponding to these hairs. Thus they are not conserved and one cannot understand them as Noether charges. They arise as coupling constants. Although there are many hairs, the black hole has only one horizon. The scalar potential becomes negative for sufficient large $$\phi $$ (or in the vicinity of black hole singularity). Therefore, the no-scalar-hair theorem does not apply to our solutions since the latter do not obey the dominant energy condition. Although the scalar potential becomes negative for sufficient large $$\phi $$ , the black holes are stable to both odd parity and scalar perturbations. As for even parity perturbations, we find there remains parameter space for the stability of the black holes. Finally, the black hole thermodynamics is developed.

Alternative for black hole paradoxes

In this paper, we investigate the exact time-dependent black hole solution on a warped five-dimensional Randall–Sundrum space–time in conformal dilaton gravity. The zeroes of the model are described by a meromorphic quintic polynomial, which has no essential singularities. The quintic equation can be reduced to the Brioschi form by means of the Weierstrass elliptic curve over [Formula: see text]. The model fits the antipodal boundary condition, i.e. antipodal points in the projected space are identified using the embedding of a Klein surface in [Formula: see text], using the [Formula: see text] symmetry on the two sides of the brane. If one writes [Formula: see text], [Formula: see text], with [Formula: see text] the normal to the brane and [Formula: see text] the dilaton field, then [Formula: see text] is conformally flat. It is the contribution from the bulk which determines the real pole on the effective four-dimensional space–time. There is no objection applying ’t Hooft’s back reaction method in constructing the unitary S-matrix for the Hawking radiation. Again, there is no “inside” of the black hole. The zeroes can also be analyzed by the icosahedron equation and by the Hopf-fibration of the Klein surface.

Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings

We construct an exact black hole solution for the Einstein gravity coupled with the nonlinear electrodynamics (which corresponds to the Maxwell electrodynamics in the weak field limit) in the presence of a cloud of strings as the source. We study the thermodynamical properties of the black hole solutions and derive the corrected first-law of thermodynamics. The presence of a cloud of strings does not affect the stability of the present black hole. However, a second-order phase transition exists for this system at a critical horizon radius. Furthermore, we study the quasinormal modes and their shadow radius. In addition, we find that, upon variation, the parameters of the theory show different aspects of the optical characteristics of the black hole solutions.

Linear perturbations of Einstein-Gauss-Bonnet black holes

We study linear perturbations about non rotating black hole solutions in scalar-tensor theories, more specifically Horndeski theories. We consider two particular theories that admit known hairy black hole solutions. The first one, Einstein-scalar-Gauss-Bonnet theory, contains a Gauss-Bonnet term coupled to a scalar field, and its black hole solution is given as a perturbative expansion in a small parameter that measures the deviation from general relativity. The second one, known as 4-dimensional-Einstein-Gauss-Bonnet theory, can be seen as a compactification of higher-dimensional Lovelock theories and admits an exact black hole solution. We study both axial and polar perturbations about these solutions and write their equations of motion as a first-order (radial) system of differential equations, which enables us to study the asymptotic behaviours of the perturbations at infinity and at the horizon following an algorithm we developed recently. For the axial perturbations, we also obtain effective Schrödinger-like equations with explicit expressions for the potentials and the propagation speeds. We see that while the Einstein-scalar-Gauss-Bonnet solution has well-behaved perturbations, the solution of the 4-dimensional-Einstein-Gauss-Bonnet theory exhibits unusual asymptotic behaviour of its perturbations near its horizon and at infinity, which makes the definition of ingoing and outgoing modes impossible. This indicates that the dynamics of these perturbations strongly differs from the general relativity case and seems pathological.

Hawking evaporation, shadow images, and thermodynamics of black holes through deflection angle

We study the Hawking evaporation process of the exact black hole with nonlinear electrodynamics for positive and negative coupling constant zeta . We provide a new perspective to study the thermodynamics of exact black hole through deflection angle formalism. We also evaluate the shadow images in the presence of deflection images for this black hole. Moreover, we consider the Gibbs energy optical dependence to investigate the Hawking-Page transition. We observe that evaporation rate depends upon zeta and black hole evaporates more quickly for positive zeta as compared to negative zeta . For the case zeta =-1, the black hole’s lifetime become infinite, which makes the black hole a remnant and the third law of black hole thermodynamics holds in this scenario. We show that the thermal variations in the deflection angle can be used to determine the stable and unstable phases of the black hole. Our findings show that large and small phase transitions of black hole occur at a specific value of the deflection angle.

Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor

General relativity admits a plethora of exact compact object solutions. The augmentation of Einstein’s action with non-minimal coupling terms leads to modified theories with rich structure, which, in turn, provide non-trivial solutions with intriguing phenomenology. Thus, assessing their viability under generic fluctuations is of utmost importance for gravity theories. We consider static and spherically-symmetric solutions of a Horndeski subclass which includes a massless scalar field non-minimally coupled to the Einstein tensor. Such theory possesses second-order field equations and admits an exact black hole solution with scalar hair. Here, we study the stability of such solution under axial gravitational perturbations and find that it is linearly stable. The qualitative features of the ringdown waveform depend solely on the ratio of the two available parameters of spacetime, namely the black hole mass m and the non-minimal coupling strength ell _eta . Finally, we demonstrate the gravitational-wave ringdown transitions between three distinct patterns as the ratio m/ell _eta increases; a state which is dominated by photon-sphere excitations and maintains a typical quasinormal ringdown, an intermediate long-lived state which exhibits gravitational-wave echoes and, finally, a state where the ringdown and echoes are depleted rapidly to turn to an exponential tail.

Closed conformal Killing–Yano initial data

Through an exhaustive search, we produce a five-parameter family of propagation identities for the closed conformal Killing–Yano (cCYK) equation on two-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension n > 4. It is well-known that spacetimes admitting a non-degenerate two-form of this type are exhausted by the Kerr-NUT-(A)dS family of exact higher dimensional black hole solutions. As a consequence, we identify a set of necessary and sufficient conditions ensuring that the cosmological vacuum development of an initial data set for Einstein’s field equations admits a cCYK two-form. We refer to these conditions as closed conformal Killing–Yano initial data equations. The four-dimensional case is special and is treated separately, where we can also handle the conformal Killing–Yano equation without the closed condition.

Dyonic black holes in nonlinear electrodynamics from Kaluza–Klein theory with a Gauss–Bonnet term

Five-dimensional Kaluza–Klein theory with an Einstein–Gauss–Bonnet Lagrangian induces nonlinear corrections to the four-dimensional Maxwell equations, which however remain second-order. Although these corrections do not have effect on the purely electric or magnetic monopole solutions for pointlike charges, they affect the dyonic solutions, smoothing the electric field at the origin for positive values of the Gauss–Bonnet coupling constant. We investigate these solutions in flat space, and then extend them in the presence of a minimal coupling to gravity, obtaining exact charged black hole solutions that generalize the Reissner–Nordström metric.

Nonsingular Black Holes in 4D Einstein–Gauss–Bonnet Gravity

Recently, several methods have been proposed to regularize a D→4 limit of Einstein–Gauss–Bonnet (EGB), leading to nontrivial gravitational dynamics in 4D. We present an exact nonsingular black hole solution in the 4D EGB gravity coupled to non-linear electrodynamics and analyze their thermodynamic properties to calculate precise expressions for the black hole mass, temperature, and entropy. Because of the magnetic charge, the thermodynamic quantities are corrected, and the Hawking–Page phase transition is achievable with diverges of the heat capacity at a larger critical radius r=r+C in comparison to the 5D counterpart where the temperature is maximum. Thus, we have a black hole with Cauchy and event horizons, and its evaporation leads to a thermodynamically stable extremal black hole remnant with vanishing temperature, and its size is larger than the 5D counterpart. The entropy does not satisfy the usual exact horizon Bekenstein–Hawking area law of general relativity with a logarithmic area correction term.

Thermodynamics of charged black holes with Maxwell and Born–Infeld fields in massive gravity theory

In the framework of massive gravity theory which is coupled to the Maxwell and Born–Infeld electrodynamics, we review derivation of the exact four-dimensional black hole solutions by use of a static and spherically symmetric geometry. The exact solutions are asymptotically AdS and show two-horizon, one-horizon, extreme and black holes without horizon. The Maxwell and Born–Infeld black hole solutions are compatible in the limit of large nonlinearity parameter and, both reduce to the Reissner–Nordström black hole in the absence of massive gravitons. By reviewing thermodynamic and conserved quantities, and making use of a Smarr-type mass formula, we check validity of the thermodynamical first law for both of Maxwell and Born–infeld black holes. We investigate thermal stability of the black holes by use of the canonical ensemble and geometrical approaches, separately. By calculating the specific heats and Ricci scalars of alternative thermodynamic metrics, we compare the results of geometrothermodynamics with those of canonical ensemble method. Also, we perform a global stability analysis by use of the grand canonical ensemble and noting the Gibbs free energy of the Maxwell and Born–Infeld black holes.

Reentrant phase transitions in Einstein-Maxwell-scalar black holes

We consider how scalar fields affect the thermodynamic behavior of charged anti-de Sitter (AdS) black holes. We specifically investigate a class of (3+1)-dimensional exact hairy charged AdS black hole solutions to Einstein-Maxwell-scalar gravity, whose stable ground state and finite horizon area in the zero temperature limit make it of particular interest. We find that the reverse isoperimetric inequality is satisfied for this class and that there exists an intermediate range of the charge that admits reentrant phase behavior, the first example of this type of phase behavior in (3+1) dimensions in a consistent theory.

Einstein-Gauss-Bonnet gravity coupled to bumblebee field in four dimensional spacetime

We study Einstein-Gauss-Bonnet gravity coupled to a bumblebee field which leads to a spontaneous Lorentz symmetry breaking in the gravitational sector. We obtain an exact black hole solution and a cosmological solution in four dimensional spacetime by a regularization scheme. We also obtain a Schwarzschild-like bumblebee black hole solution in D-dimensional spacetime. We find that the bumblebee field doesn't affect the locations of the black hole horizon, but only affects the gravitational potential. That is, its gravitational potential has a minimum value (negative) in the black hole interior and has a positive value 1+ℓ at short distance r→0. If the constant ℓ is large enough, then this kind of black hole is practically free from the singularity problem. The thermodynamics and phase transition are also studied. In a cosmological context, it is interesting that the Gauss-Bonnet term has no effect on the conservation of energy equation. A late-time expansion of de Sitter universe can be replicated in an empty space. The Gauss-Bonnet term and the bumblebee field can both actually act as a form of dark energy.

Schwarzschild-like black hole with a topological defect in bumblebee gravity

In this paper, we derive an exact black hole spacetime metric in the Einstein–Hilbert–Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss–Bonnet theorem, we calculate the deflection angle in weak field limits and we discuss the possibility of testing the effect of global monopole field and bumblebee field, on a weak deflection angle. We find that the global monopole parameter and also Lorentz symmetry breaking parameter has an increasing effect on the deflection angle.

Bound orbits around charged black holes with exponential and logarithmic electrodynamics

We present exact black hole solutions endowed with magnetic charge coming from exponential and logarithmic nonlinear electrodynamics (NLED). Classically, we analyze the null and timelike geodesics, all of which contain both the bound and the scattering orbits. Using the effective geometry formalism, we found that photon can have nontrivial stable (both circular and non-circular) bound orbits. The noncircular bound orbits for the one-horizon case mostly take the form of precessed ellipse. For the extremal and three-horizon cases we find many-world orbits where photon crosses the outer horizon but bounces back without hitting the true (or second, respectively) horizon, producing the epicycloid and epitrochoid paths.Semiclassically, we investigate their Hawking temperature, stability, and phase transition. The nonlinearity enables black hole stability with smaller radius than its RN counterpart. However, for very-strong nonlinear regime, the thermodynamic behavior tends to be Schwarzschild-like.

Exploring the black hole spectrum of axionic Horndeski theory

We provide a ``user-friendly'' algorithm to systematically and rapidly obtain exact planar black hole solutions in the Einstein-Maxwell theory deformed by the most general shift- and reflection-symmetric Horndeski sector where the usual Galileon is replaced by a tuple of scalars with profiles linear in the coordinates of the transverse manifold. Under precise assumptions, these axion backgrounds break the translational invariance of the system, causing momentum dissipation in the holographically dual field theory. The success of the method relies on the simple realization that the bulk equations of motion become more tractable when written in terms of the axions kinetic terms, instead of the radial coordinate. Showcasing this particularly efficient recipe, we derive novel asymptotically AdS black holes, and show that their extremal counterparts always flow to an $\mathrm{AdS}_2\times \mathbb{R}^2$ infrared fixed point. Additionally, we report an interesting family of new asymptotically Lifshitz black hole solutions with $z>1$. Finally, we discuss the DC transport properties of the dual relativistic field theories in view of possible applications to condensed matter systems.

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.

Formula omitted] AdS Einstein–Gauss–Bonnet black hole with Yang–Mills field and its thermodynamics

We derive an exact black hole solution for the Einstein–Gauss–Bonnet gravity with Yang–Mills field in 4D AdS spacetime and investigate its thermodynamic properties to calculate exact expressions for the black hole mass, temperature, entropy and heat capacity. The thermodynamic quantities get modification in the presence of Yang–Mills field, however, entropy remains unaffected by the Yang–Mills charge. The solution exhibits P−v criticality and belongs to the universality class of Van der Waals fluid. We study the effect of Gauss–Bonnet coupling and Yang–Mills charge on the critical behaviour and black hole phase transition. We observe that the values of critical exponents increase with the Yang–Mills charge and decrease with the Gauss–Bonnet coupling constant.

Exact black hole solutions with a conformally coupled scalar field and dynamic Ricci curvature in f(R) gravity theories

We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in f(R) gravity. We first consider the asymptotically flat model f(R) = R -2alpha sqrt{R} and derive an exact black hole solution. Then, we consider the asymptotically (A)dS model f(R) =R -2 Lambda -2 alpha sqrt{R-4 Lambda } and derive an exact black hole solution. In both cases the modified gravity parameter alpha , which has the dimension of the inverse mass, cannot be set to zero and the self-interacting potential is determined from the Klein–Gordon equation, preserving the conformal invariance. The thermodynamics of the solutions is also studied.

Black holes with many horizons in the theories of nonlinear electrodynamics

In this article, we construct exact black hole solutions with many horizons (more than two) in the Einstein-nonlinear electrodynamic theories. In particular, we acquire the explicit expression of a nonlinear electrodynamic Lagrangian for the 3-horizon black holes. Then we make the investigations of three-horizon black holes on the horizons, the null and timelike geodesics, the Love numbers, and the thermodynamics.

Three-dimensional massive Kiselev AdS black hole and its thermodynamics

We present an exact three-dimensional massive Kiselev AdS black hole solution. This Kiselev black hole is neither perfectly fluid, nor is it the quintessential solution, but the BTZ black hole modified by the anisotropic matter. This black hole possesses an essential singularity at its radial origin and a single horizon whose radius will increase monotonically when the parameter of the anisotropic matter field ω decreases. We calculate all thermodynamic quantities and find that the first law of thermodynamics of this massive Kiselev AdS black hole can be protected, while the consistent Smarr formula is only held in the extended thermodynamic phase space. After examining the sign of free energy, we conclude that there is no Hawking-Page transition since the massive Kiselev AdS black hole phase is always thermodynamically favored. Moreover, we study the phase transition between the Kiselev AdS black hole and BTZ black hole by considering the matchings for their temperature. We find that the Kiselev AdS black hole is still a thermodynamically more preferred phase, because it always has a smaller amount of free energy than the BTZ black hole, which seems to indicate that the anisotropic matter field may emerge naturally in BTZ black hole spacetime under some thermal fluctuations. We also show a first order phase transition between the Kiselev AdS black hole phase with and the black hole phase with . As the Kiselev AdS black hole has some notable features on the phase transition of black holes in three dimensions, it provides important clues to further investigate these both surprising and similar behaviors in four and higher dimensions.