We consider a three-dimensional rotating Hořava AdS black hole, that corresponds to a Lorentz-violating version of the BTZ black hole and we analyze the effect of the breaking of Lorentz invariance on the possibility that the black hole can acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizons. We find that the critical angular momentum of particles increases when the Hořava parameter $ξ$ increases and when the aether parameter $b$ increases. Also, the particles can collide on the inner horizon with arbitrarily high CM energy if one of the particles has a critical angular momentum being possible the BSW process, for the non-extremal rotating Hořava AdS black hole. Mainly, while that for the extremal BTZ black hole the particles with critical angular momentum only can exist on the degenerate horizon, for the Lorentz-violating version of the BTZ black hole the particle with critical angular momentum can exist in a region from the degenerate horizon.
This paper presents a new metric for slowly rotating charged Gauss-Bonnet black holes in higher dimensional anti-de Sitter spaces. Taking the angular momentum parameter $a$ up to second order, the slowly rotating charged black hole solutions are obtained by working directly in the action.
The imposition of a constraint between the metric tensor elements in both three- and four-dimensional, rotating AdS space-times is shown to reduce the number of independent equations of motion and to result in new families of solutions to the equations of motion. For the geometries investigated analytic solutions or partial analytic solutions of the equations of motion are obtained. In all cases the number of independent field equations is less than the number of independent functions, resulting in an undetermined function which can be freely specified. For rotating, asymptotically $AdS$ space…
In this paper, with an appropriate combination of three Liouville-type dilaton potentials, we obtain the higher dimensional charged slowly rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime. The angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton coupling constant. It is shown that the dilaton field modifies the gyromagnetic ratio of the rotating dilaton black holes.
We study the motion of particles in the background of a three-dimensional rotating Hořava AdS black hole that corresponds to a Lorentz-violating version of the BTZ black hole and we analyze the effect of the breaking of Lorentz invariance in such motion by solving analytically the geodesic equations. Mainly, we find that Lorentz-violating version of the BTZ black hole posses a more rich geodesic structure, where the planetary and circular orbits are allowed, which does not occurs in the BTZ background.
We derive mass-independent equations and inequalities for Kerr-Newman-anti-de Sitter black holes. In particular, we obtain an equation that relates electric charge, angular momentum and the areas of the event and Cauchy horizons. An area-angular momentum-charge inequality is derived from this formula, which becomes an equality in the degenerate limit. The same equation is shown to hold for arbitrary degenerate black holes, which might, for example, be surrounded by matter.
The presence of a photon region around the black hole is an essential feature in receiving the emitted spectrum from the vicinity of the black hole by the distant observer. In this paper, we investigate the optical properties of rotating regular anti-de Sitter (AdS) black holes, which characterized by its mass $(M)$, spin parameter $(a)$, deviation parameter $(k)$ and the cosmological constant $(Λ)$ related to the curvature radius via $(Λ=-3/l^2)$. We derive the complete null geodesic equations of motion and study the unstable circular orbits for an observer at given Boyer-Lindquist coordinate…
In this paper, the author study the throttling process of the Rotating Bardeen-AdS black hole in a systematic way. In the exended phase space, the mass of black holes should be viewed as entheply. We derive the Joule-Thomson coefficient $μ$ explicitly, and with numerical method, we depict the inversion curves and isenthalpic curves with different parameter $J$ and $g$. It is found that there are only minimum inversion temperature but no maximum inversion temperture, and the ratio between minimum inversion temperature $T_{min}$ and critical temperature $T_C$ is a little greater than $1/2$, and …
By using the scaling symmetry in the reduced action formalism, we derive the novel Smarr relation which holds even for the hairy rotating AdS_3 black holes. And then, by using the Smarr relation we argue that the hairy rotating AdS_3 black holes are stable thermodynamically, compared to the non-hairy ones.
A series of corrections to general relativity have recently been applied to find the relationship between entropy and extremality-bound black holes. This relationship has been investigated for many black holes, such as charged AdS, rotating, and massive gravity black holes. We give a minor constant correction to the action and confirm these universal relations for a charged-rotating-AdS black hole. We then examine these calculations for the black hole, surrounded by the quintessence and the cloud of string. In this paper, we evaluate a new universal relation. It means that we find the relation…
In this paper, we consider a charged rotating AdS black holes in four dimensions and study the effects of leading-order thermal corrections on the thermodynamics of such system explicitly. The first-order corrected thermodynamical quantities also satisfy the first-law of thermodynamics of the black holes. The holographic duality between the charged rotating AdS black holes and Van der Waals fluid is also emphasized through the $P-v$ diagram. Finally, we study the effects of the leading-order thermal corrections on the stability of the charged rotating black holes.
Using the Hamilton-Jacobi method, we study certain optical shadows of rotating Bardeen-AdS black holes in the presence of internal and external field contributions. Precisely, we examine the shadow using one-dimensional real curves. By establishing the equations of motion of such AdS black holes without external dark sectors, we first analyze the shadow configurations in terms of a reduced moduli space involving only internal parameter contributions including the charge of the nonlinear electrodynamics. Among others, we find that this parameter serves as a geometric quantity controlling the sh…
If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz group, we find interesting one-parameter families of stationary vacua in three-dimensional anti-de Sitter space. In particular, there exists a family of rotating Rindler vacua, labeled by the rotation parameter beta, which are related to the usual Rindler vacuum by non-trivial Bogolubov transformations. Rotating Rindler-AdS space possesses not only an observer-de…
We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance …
We generalize the vacuum static black brane solutions of Einstein's equations with negative cosmological constant recently discussed in literature, by introducing rotations and an electromagnetic field. We investigate numerically the thermodynamical properties of the charged and of the rotating $AdS$ black brane and we provide evidences for the existence of the charged and rotating case. In particular, we study the influence of the rotation and charge on the tension and mass. We find that the rotation essentially influences the tensions while the charge essentially influences the mass.
Quadratic Curvature Correction to the Euclidean Action of Rotating AdS Black Holes in General Dimensions
The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）；Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）
In this report the exact rotating charged black hole solution to the Einstein--nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic charges, cosmological constant $Λ$, and three parameters due to the nonlinear electrodynamics: $β$ is associated to the potential vectors $A_μ$ and ${}^{\star}P_μ$, and two constants, $F_0$ and $G_0$, due to the presence of the invariants $F$ and $G$ in the Lagrangian $L(F(\,x^μ),G(\,x^μ))$. This solution is of Petrov type D, characterized by the Weyl tensor eig…
To provide an analytic verification of the nature of phase transition at the critical point of $P-V$ criticality, the original expressions of Ehrenfest equations have been introduced directly. By treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume respectively, we carry out analytical check of classical Ehrenfest equations. To show that our approach is universal, we investigate not only higher-dimensional charged AdS black holes, but also rotating AdS black holes. Not only are the examples of Einstein gravity shown, but also the example of modifie…
We obtain the charged rotating black hole in conformal gravity. The metric is asymptotic to the (anti-)de Sitter spacetime. The contribution to the metric from the charges has a slower falloff than that in the Kerr-Newman AdS black hole. We analyse the global structure and obtain all the thermodynamical quantities including the mass, angular momentum, electric/magnetic charges and their thermodynamical conjugates. We verify that the first law of thermodynamics holds. We also obtain the new neutral rotating black holes that are beyond Einstein metrics. In contrast to the static ones, these rota…
We find that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value and the shadowless-ness may be related to the appearance of the null hypersurface caustics (NHC) both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
In [Phys. Rev. Lett. 124, 101103 (2020)], a universal relation between corrections to entropy and extremality was proposed. The relation was also found to exactly hold for the four-dimensional charged AdS black hole. In this paper, we extend the study to the rotating BTZ and Kerr-AdS black holes when a constant correction to General Relativity is considered for the first time. The entropy and extremality bound are calculated, and they have a closely dependent behavior with the coupling parameter of the constant correction. We confirm the universal relation for the rotating AdS black holes. Fur…
Force-Free Electrodynamics for black holes in Anti de Sitter is considered. We present new, energy extracting solutions of Force-Free Electrodynamics in Anti de Sitter - Near Horizon Extremal Kerr and Super-Entropic Near Horizon Extremal Kerr geometries. The relevant equations of motion are derived from an action for force-free plasma surrounding spinning black holes with generic asymptotics. We consider the energy flux of electrodynamic fields in rotating frames to argue that the correct measure for energy extraction is the energy flux measured by a rotating observer in the near horizon regio…
Classical Censorship permits AdS$_5$-Kerr black holes with arbitrarily large angular momenta per unit mass, which does not seem reasonable from a holographic point of view. However, it has been shown that, when these black holes are embedded in string theory, their angular momentum per unit mass is in fact bounded by $2\sqrt{2}L$, where $L$ is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS$_5$-Kerr black holes, with angular momentum per unit mass close to this bound, might be unstable, for example, to a superradiant instability. We show that this is not al…
A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the …
We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a more general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against superradiant modes under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude $ε$ of the scalar field, up to $O(ε^4)$. The lumps of non-linearly perturbed geometry admit only one Killing…
Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS black hole. Treating the entropy and pressure as the fluctuation coordinates, we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the use of the Christodoulou-Ruffini-like squared-mass formula, which is quite different from the charged case. Employing the empirical obse…
We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation paramet…
We obtain a perturbative solution for rotating charged black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to forth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Ch…
We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries (with non-toroidal horizon topology) and all static near-horizon geometries for black holes of this kind. This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS(4) rotating extremal black hole, is the near-horizon limit of extremal Kerr-Newman-AdS(4). We also identify the subset of near-horizon geometries which are supersymmetric. Finally, …
We study the motion of photons in the background of a three-dimensional rotating Hořava AdS black hole that corresponds to a Lorentz-violating version of the BTZ black hole and we analyze the effect of the breaking of Lorentz invariance on the null geodesics structure, by solving analytically the equations of motion. Mainly we find that, through a fine tuning of the parameters of the theory, new kinds of orbits are allowed, such as unstable circular orbits and trajectories of first kind. Also, we show that an external observer will see that photons arrive at spatial infinity in a finite coordi…
We study the thermodynamics of higher-dimensional singly spinning asymptotically AdS black holes in the canonical (fixed J) ensemble of extended phase space, where the cosmological constant is treated as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Along with the usual small/large black hole phase transition, we find a new phenomenon of reentrant phase transitions for all d>5 dimensions, in which a monotonic variation of the temperature yields two phase transitions from large to small and back to large black holes. This situation is similar to that …
Using the AdS/CFT correspondence we consider the retarded Green's function in the background of rotating near-extremal AdS$_4$ black holes. Following the canonical AdS/CFT dictionary into the asymptotic boundary we get a CFT$_3$ result. We also take a new route and zoom in on the near-horizon region, blow up this region and show that it yields a CFT$_2$ result. We argue that the decoupling of the near-horizon region is akin to the decoupling of the near-throat region of a D3-brane, which led to the original formulation of the AdS/CFT correspondence, thus implying that the Kerr/CFT corresponden…
We show that there are two or more procedures to generalize the known four-dimensional transformation, aiming to generate cylindrically rotating charged exact solutions, to higher dimensional spacetimes . In the one procedure, presented in Eur. Phys. J. C (2019) \textbf{79}:668, one uses a non-trivial, non-diagonal, Minkowskian metric $\barη_{ij}$ to derive complicated rotating solutions. In the other procedure, discussed in this work, one selects a diagonal Minkowskian metric $η_{ij}$ to derive much simpler and appealing rotating solutions. We also show that if ($g_{μν},\,η_{ij}$) is a rotati…
We present results from a numerical study of rotating black hole formation in 3-dimensional asymptotically anti-de Sitter (AdS) spacetime, focusing on the structure of the black hole interior. While black holes in $AdS_3$ are of theoretical interest for a wide variety of reasons, we choose to study this system primarily as a toy model for astrophysical (4-dimensional) black holes formed from gravitational collapse. We investigate the effect of angular momentum on the geometry inside the event horizon, and see qualitative changes in the interior structure as a function of the spin parameter. Fo…
I construct exact solutions for general nonextremal rotating, charged Kaluza-Klein black holes with a cosmological constant and with arbitrary angular momenta in all higher dimensions. I then investigate their thermodynamics and find their generalizations with the NUT charges. The metrics are given in both Boyer-Lindquist coordinates and a form very similar to the famous Kerr-Schild ansatz, which highlights its potential application to include multiple electric charges into solutions yet to be found in gauged supergravity. It is also observed that the metric ansatz in $D = 4$ dimensions is sim…
We compute the quasinormal modes (QNMs) of a massive scalar field in the background of a rotating three-dimensional Hořava AdS black hole, and we analyze the effect of the breaking of the Lorentz invariance on the QNMs. Imposing on the horizon that there are only ingoing waves and at infinity the Dirichlet boundary conditions and the Neumann boundary condition, we calculate the oscillatory and the decay modes of the QNMs. We find that the propagation of the scalar field is stable in this background and employing the holographic principle we find the different times of the perturbed system to r…
Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets were classified, we construct genuine rotating supersymmetric black holes in AdS(4) with nonconstant scalar fields. This is done for the SU(1,1)/U(1) model with prepotential F=-iX^0X^1. In the static case, the black holes are uplifted to eleven dimensions, and generalize the solution found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. The constructed rotating black holes preserve…
We extend to study Hawking radiation via tunneling in conformal gravity. We adopt Parikh-Wilczek's semi-classical tunneling method and the method of complex-path integral to investigate Hawking radiation from new rotating AdS black holes in conformal gravity. In this paper, the research on Hawking radiation from the rotating black holes is done in a general system, not limited in dragging coordinate systems any longer. Moreover, there existed some shortcomings in the previous derivation of geodesic equations. Different from the massless case, they used a different approach to derive the geodes…
A new rotating axionic AdS$_4$ black hole dressed with a scalar field
Universidad Católica del Maule（天主教马乌莱大学）；Damghan University（达姆甘大学）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；Universidad Nacional Autónoma de Honduras（洪都拉斯国立自治大学）；Benemérita Universidad Autónoma de Puebla（普埃布拉自治优秀大学）；Universidad de Antioquia（安蒂奥基亚大学）
One of the solutions of Einstein field equation with cylindrical symmetry is known as black string solution. In this work, the rotating black string solution in dRGT massive gravity is obtained and then called rotating-dRGT black string solution. This solution is a kind of generalized version of rotating AdS/dS black sting solution containing an additional two more terms characterizing the structure of graviton mass. The horizon structures of the black string are explored. The thermodynamical properties of the black string are investigated. We found that it is possible to obtain the Hawking-Pa…
We study the stability of charged rotating black holes in a consistent truncation of Type $IIB$ Supergravity on $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface-like operators in a subsector of ${\cal N}=4$ SYM. By solving the equation of motion for a massless scalar field in this background, using matched asymptotic expansion followed by a numerical solution scheme, we are able to compute its Quasi-Normal modes, and analyze it's regime of (in)stability. …
We study the holographic duals of bosonic and fermionic fields and compute their Quasinormal Frequencies (QNF) by exploiting that they are massive charged fields in $\mathrm{AdS_2 \times \mathcal{K}}$. In particular, we assess the stability of the scalar and fermionic operators in Myers-Perry's black holes with equal angular momenta. We compute the central charge and the Hawking-entropy and introduce extremality parameters to determine the properties of the dual CFT. Then, we briefly discuss how detection of Spin-2 fields can pave the way for more deep understanding of the holographic principl…
We study the AdS rotating black hole solution for the Bergshoeff-Hohm-Townsend (BHT) massive gravity in three dimensions. The field equations of the asymptotically AdS black hole of the static metric can be expressed as the first law of thermodynamics, i.e. $dE=TdS-PdV$. The corrected Hawking-like temperature and entropy of asymptotically AdS rotating black hole are calculated using the Cardy formula and the tunneling method. Comparison of these methods will help identify the unknown leading correction parameter $β_1$ in the tunneling method.
We obtain retarded Green's functions for massless scalar fields in the background of near-extreme, near-horizon rotating charged black holes of five-dimensional minimal gauged supergravity. The radial part of the (separable) massless Klein-Gordon equation in such general black hole backgrounds is Heun's equation, due to the singularity structure associated with the three black hole horizons. On the other hand, we find the scaling limit for the near-extreme, near-horizon background where the radial equation reduces to a Hypergeometric equation whose $SL(2,{\bf R})^2$ symmetry signifies the unde…
We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS$_5$ black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined, on the field theory side, by the superconformal index and the refined topologically twisted index of $\mathcal{N}=4$ supersymmetric Yang-Mills theory, respectively. We read off the logarithmic correction from those field-theoretic partition functions. On the gravity side, we take the near-horizon limit and apply the Kerr/CFT correspondence whose associated ch…
With the help of a generalized form of the metric ansatz found for the single-charge case in a previous work [S.Q. Wu, Phys. Rev. D 83, 121502(R) (2011)], I adopt a simple algorithm to construct the most general nonextremal rotating charged black hole solutions in five-dimensional $U(1)^3$ gauged supergravity. The general solution that is interesting for testing the AdS$_5$/CFT$_4$ correspondence in M-theory, is characterized by its mass, two unequal rotation parameters, three different U(1) charges, and a negative cosmological constant. The metric ansatz is very universal and illuminative, it…
Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher dimensions, focusing on slowly rotating charged AdS black holes with a single angular momentum. We divide the spacetime of these black holes into the near-horizon and far regions and find solutions to the scalar wave equation in each of these regions. Next, we perform the matching of these solutions in the overlap between the regions, by employing the idea that …
We present new rotating black brane solutions which solve Einstein's equations with cosmological constant $Λ$ in arbitrary dimension $d$. For negative $Λ$, the branes naturally appear in AdS supergravity compactifications, and should therefore play some role in the AdS/CFT correspondence. The spacetimes are warped products of a four-dimensional part and an Einstein space of dimension $d-4$, which is not necessarily of constant curvature. As a special subcase, the solutions contain the higher dimensional generalization of the Kerr-AdS metric recently found by Hawking et al.
