We consider the asymptotically flat double-Kerr solution for two equal mass black holes with either the same or opposite angular momentum and with a massless strut between them. For fixed angular momentum and mass, the angular velocity of two co-rotating Kerr black holes decreases as they approach one another, from the Kerr value at infinite separation to the value of a single Kerr black hole with twice the mass and the angular momentum at the horizons merging limit. We show that the ratio J/M^2 for extremal co-rotating Kerr black holes varies from unity at infinite separation to two at the merging limit. These results are interpreted in terms of rotational dragging and compared with the case of counter-rotating Kerr black holes. We then analyse the merging of ergo-regions. In the co-rotating case the merger point occurs at an angle of π/2, in agreement with recent general arguments. In the counter-rotating case the ergo-regions never merge. We study the horizon geometry for both cases as a function of the distance and provide embedding diagrams. Finally, we study the thermodynamical evolution of the co-rotating double Kerr system, showing that, in the canonical ensemble, it is thermodynamically stable for fast spinning black holes. As for single Kerr black holes the stable and unstable phases are separated by a second order phase transition. We show that for large fixed angular momentum two Kerr black holes reach a minimum distance, before horizon merging has occurred, where the thermodynamical approximation breaks down. We also consider the micro-canonical ensemble to study the maximal energy that can be extracted from the double Kerr system as a function of the separation between the black holes.
We investigate phase transitions and critical behaviors of the Kerr-Sen black hole in four dimensions. Computing the involved thermodynamical quantities including the specific heat and using the Ehrenfest scheme, we show that such a black hole undergoes a second-order phase transition. Adopting a new metric form derived from the Gibss free energy scaled by a conformal factor associated with extremal solutions, we calculate the geothermodynamical scalar curvature recovering similar phase transitions. Then, we obtain the scaling laws and the critical exponents, matching perfectly with mean field…
We investigate the weak cosmic censorship conjecture in extremal and near-extremal Kerr-Newman-(anti-)de Sitter black holes by the scattering of a massive scalar field with an electric charge. Under this scattering, the scalar field fluxes change the black hole state, as determined by the mass, angular momentum, and electric charge. The black hole may exceed its extremal condition because of these changes. However, we find that the black hole cannot be overcharged or overspun by the scattering. In particular, although the fluxes are closely associated with the asymptotic boundary conditions al…
We explore some (especially, thermodynamical) properties of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning counterpart, and check whether or not both black holes satisfy the first law and Bekenstein-Smarr mass formulas. To this end, new Christodoulou-Ruffini-like squared-mass formulae for the usual dyonic Kerr-Sen-AdS$_4$ solution and its ultraspinning cousin are deduced. Similar to the ultraspinning Kerr-Sen-AdS$_4$ black hole case, we demonstrate that the ultraspinning dyonic Kerr-Sen-AdS$_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since th…
We study the low-temperature limit of scalar perturbations of the Kerr-AdS$_{5}$ black-hole for generic rotational parameters. We motivate the study by considering real-time holography of small black hole backgrounds. Using the isomonodromic technique, we show that corrections to the extremal limit can be encoded in the monodromy parameters of the Painlevé V transcendent, whose expansion is given in terms of irregular chiral conformal blocks. After discussing the contribution of the intermediate states to the quasi-normal modes, we perform a numerical analysis of the low-lying frequencies. We …
Stationary axisymmetric binary configurations of unequal Kerr sources with a massless strut among them are developed in a physical representation. In order to describe interacting black holes, the axis conditions in the most general case are solved analytically deriving the corresponding $5$-parametric asymptotically flat exact solution. In addition, we obtain concise formulas for the black hole horizons, the interaction force, as well as the thermodynamical characteristics of each source in terms of physical Komar parameters: mass $M_{i}$, angular momentum $J_{i}$, and coordinate distance $R$…
In this work we have presented a special class of Kerr-Newman-NUT black hole, having its horizon located precisely at $r=2M$, for $Q^{2}=l^{2}-a^{2}$, where $M$, $l$, $a$ and $Q$ are respectively mass, NUT, rotation and electric charge parameters of the black hole. Clearly this choice radically alters the causal structure as there exists no Cauchy horizon indicating spacelike nature of the singularity when it exists. On the other hand, there is no curvature singularity for $l^2 > a^2$, however it may have conical singularities. Furthermore there is no upper bound on specific rotation parameter…
We show that the Hawking--Bekenstein entropy formula is modified by a factor of $8/3$ if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition $ε=Mc^2/V$, which is the average energy density of the Hawking radiation. This volume scales as $V \sim M^5$, agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state $S(E,V)\sim E^{3/4}V^{1/4}$. The…
In the present paper binary configurations of identical corotating Kerr-Newman black holes separated by a massless strut are derived and studied. After solving the axis conditions and establishing the absence of magnetic charges in the solution, one gets two 4-parametric corotating binary black hole models endowed with electric charge, where each source contains equal/opposite electric charge in the first/second configuration. Since the black hole horizons are given by concise expressions in terms of physical parameters, all their thermodynamical properties satisfying the Smarr relation for th…
In this paper, binary systems of unequal Kerr-Newman black holes located on the axis and apart by a massless strut are investigated. After adopting a fitting parametrization, the conditions on the axis and the one eliminating the individual magnetic charges are solved exactly with the aim to obtain a 7-parametric asymptotically flat exact solution. It is also deduced explicit analytical formulas for each half-length horizon $σ_{i}$, $i = 1,2$, in terms of arbitrary physical Komar parameters: mass $M_{i}$, electric charge $Q_{i}$, angular momentum $J_{i}$, and a coordinate distance $R$. All the…
Evidencing Quantum Gravity with Thermodynamical Observables
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）；Department of Physics, Royal Holloway, University of London（伦敦大学皇家霍洛威学院物理系）；Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna（维也纳大学物理学院维也纳量子科学与技术中心）
Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
In this paper we focus on the relation between quasinormal modes (QNMs) and a rotating black hole shadows. As a specific example, we consider the quantum deformed Kerr black hole obtained via Newman--Janis--Azreg-A\"ınou algorithm. In particular, using the geometric-optics correspondence between the parameters of a QNMs and the conserved quantities along geodesics, we show that, in the eikonal limit, the real part of QNMs is related to the Keplerian frequency for equatorial orbits. To this end, we explore the typical shadow radius for the viewing angles, $θ_0=π/2$, and obtained an interesting …
The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation $τ\times T\geq {{\hbar}\overπ}$. It is known that some perturbation modes of near-extremal Kerr black holes in the regime $MT_{\text{BH}}/\hbar\ll m^{-2}$ are characterized by normalized relaxation times $πτ\times T_{\text{BH}}/\hbar$ which, in the approach to the limit $MT_{\text{BH}}/\hbar\to0$, make infinitely many oscillations with a tiny constant amplitude around $1$ and therefore cannot be used directly to…
We report about the possibility for interacting Kerr sources to exist in two different states - black holes or naked singularities - both states characterized by the same masses and angular momenta. Another surprising discovery reported by us is that in spite of the absence of balance between two Kerr black holes, the latter nevertheless can repel each other, which provides a good opportunity for experimental detection of the spin-spin repulsive force through the observation of astrophysical black-hole binaries.
One of the most crucial areas of gravity research, after the direct observation of gravitational waves, is the possible modification of General Relativity at ultraviolet and infrared scales. In particular, the possibility of parity violation should be considered in strong field regime. The Chern-Simons gravity takes into account parity violation in strong gravity regime. For all conformally flat spacetimes and spacetimes with a maximally symmetric two-dimensional subspace, Chern-Simons gravity is identical to General Relativity. Specifically, the Anti-de Sitter (A)dS-Kerr/Kerr black hole is no…
We investigate static and rotating charged spherically symmetric solutions in the framework of $f({\cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f({\cal R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit and one that arises purely from the gravitational modification. The novel black…
Light bending around the Kerr-Bertotti-Robinson black hole using material medium approach
National Institute of Technology, Agartala（阿加塔拉国家技术学院）；The Institute of Mathematical Sciences（数学科学研究所）；Khazar University（汗扎尔大学）；Hemwati Nandan Bahuguna Garhwal University（赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Centre for Space Research, North-West University（西北大学空间研究中心）；Assam University（阿萨姆大学）
We present new equilibrium solutions of stationary models of magnetized thick disks (or tori) around Kerr black holes with synchronised scalar hair. The models reported here largely extend our previous results based on constant radial distributions of the specific angular momentum along the equatorial plane. We introduce a new way to prescribe the distribution of the disk's angular momentum based on a combination of two previous proposals and compute the angular momentum distribution outside the equatorial plane by resorting to the construction of von Zeipel cylinders. We find that the effect …
We evaluate the validity of the weak form of the cosmic censorship conjecture and the third law of black hole dynamics for Kerr-MOG black holes interacting with scalar test fields. Ignoring backreaction effects, we first show that both extremal and nearly extremal Kerr-MOG black holes can be overspun into naked singularities by scalar test fields with a frequency slightly above the superradiance limit. In addition, nearly extremal Kerr-Mog black holes can be continuously driven to extremality by test fields. Next, we employ backreaction effects based on the argument that the angular velocity o…
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $ψ_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $\ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanis…
