We discuss the "quantum deformed Schwarzschild spacetime" as originally introduced by Kazakov and Solodukhin in 1993, and investigate the precise sense in which it does and does not satisfy the desiderata for being a "regular black hole". We shall carefully distinguish (i) regularity of the metric components, (ii) regularity of the Christoffel components, and (iii) regularity of the curvature. We shall then embed the Kazakov-Solodukhin spacetime in a more general framework where these notions are clearly and cleanly separated. Finally we analyze aspects of the classical physics of these "quantum deformed Schwarzschild spacetimes". We shall discuss the surface gravity, the classical energy conditions, null and timelike geodesics, and the appropriate variant of Regge--Wheeler equation.
In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in {Friedmann-Robertson-Walker (FRW)} cosmology, where this "noncommutativity" provides a simple mechanism that can explain the origin of the cosmological constant. In this paper we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzsc…
We construct the first examples of deformed non-abelian black strings in a 5-dimensional Einstein-Yang-Mills model. Assuming all fields to be independent of the extra coordinate, we construct deformed black strings, which in the 4-dimensional picture correspond to axially symmetric non-abelian black holes in gravity-dilaton theory. These solutions thus have deformed S^2 x R horizon topology. We study fundamental properties of the black strings and find that for all choices of the gravitational coupling two branches of solutions exist. The limiting behaviour of the second branch of solutions ho…
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
Inspired by the Einstein-Born-Infeld black hole, we introduce the isolated horizon to study the Kehagias-Sfetsos (KS) black hole in the deformed Hořava-Lifshitz gravity. This is because the KS black hole is more close to the Einstein-Born-Infeld black hole than the Reissner-Nordström black hole. We find the horizon and ADM masses by using the first law of thermodynamics and the area-law entropy. The mass parameter $m$ is identified with the quasilocal energy at infinity. Accordingly, we discuss the phase transition between the KS and Schwarzschild black holes by considering the heat capacity a…
We study the quasinormal modes of the massless scalar perturbation in the background of a deformed black hole in the Hořava-Lifshitz gravity with coupling constant $λ=1$. Our results show that the quasinormal frequencies depend on the parameter in the Hořava-Lifshitz gravity and the behavior of the quasinormal modes is different from those in the Reissner-Norstr\"{om} and Einstein-Born-Infeld black hole spacetimes. The absolute value of imaginary parts is smaller and the scalar perturbations decay more slowly in the deformed Hořava-Lifshitz black hole spacetime. This information can help us un…
We find generators of the conformal symmetry for the class of Kerr-Newman-NUT-AdS black holes from the deformed scalar probe equation. We find two classes of solutions for the generators (also known as conformal J and Q pictures). The two classes of deformed generators are the extension of similar generators for the regular conformal symmetry. Moreover, we find that the two pictures can be generalized and extended into a general picture. In each picture, the generators produce an extended local family of SL(2,R)_L \times SL(2,R)_R hidden conformal symmetries for the Kerr-Newman-NUT-AdS black h…
A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal. The classical singularity present in the classical geometry is resolved by the deformation, so that propagation of a wave-packet can be continued through the classically singular region, ultimately reaching another asymptotically ``flat'' region.
Using perturbative techniques, we investigate the existence and properties of a new static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild-anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces--i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon o…
A family of deformed AdS4-Reissner-Nordström black branes, governed by a free parameter, is derived using the ADM formalism, in the context of the membrane paradigm. Their new event horizons, the Hawking temperature and other aspects are scrutinized. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio for the deformed AdS4-Reissner-Nordström metric. The Killing equation is shown to yield new values for the free parameter and the shear viscosity-to-entropy ratio is used to derive a reliable range for tidal charge.
The motion of a massive test particle around a Kehagias-Sfetsos black hole in deformed Hourava-Lifshitz gravity is studied. Employing the effective potential, the marginally bound orbits and the innermost stable circular orbits are analyzed. For the marginally bound orbits, their radius and angular momentum decrease with the parameter $ω$ of the gravity. For the innermost stable circular orbits, the energy and angular momentum also decrease with $ω$. Based on these results, we investigate the periodic orbits in the Kehagias-Sfetsos black holes. It is found that the apsidal angle parameter incr…
In this paper, a four dimensional rotating Kaluza Klien (K-K) black hole was deformed using rainbow functions derived from loop quantum gravity and non-commutative geometry. We studied the thermodynamic properties and critical phenomena of this deformed black hole. The deformed temperature and entropy showed the existence of a Planckian remnant. The calculation of Gibbs free energy $ G$ for the ordinary and deformed black holes showed that both share a similar critical behaviour.
A family of deformed AdS$_5$-Schwarzschild black branes is here derived, employing the membrane paradigm of AdS/CFT. The solution of the Einstein-Hilbert action, with the Gibbons-Hawking term and a counter-term that eliminates eventual divergences, yields a partition function associated with the dual theory which allows the computation of the entropy, pressure and free energy, as state functions, in the canonical ensemble. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio, then restricting the range of the parameter that defines a family of defor…
It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black-hole remnants of the order of the Planck-mass. Usually this sort of QFTs are endowed with two specific features, the modified dispersion relation, which is universal, and the concept of minimum length, which, however, is not universal. While the emergence of the minimum-length most readily leads to the idea of the black hole remnants, here we examine the behaviour of the potential that follows …
We investigate the thermodynamic geometry and phase transition of Kehagias-Sfetsos black hole in the deformed Horava-Lifshitz gravity with coupling constant $λ=1$. The phase transition in black hole thermodynamics is thought to be associated with the divergence of the capacities. And the structures of these divergent points are studied. We also find that the thermodynamic curvature produced by the Ruppeiner metric is positive definite for all $r_+ > r_-$ and is divergence at $η_2=0$ corresponded to the divergent points of $C_Φ$ and $C_T$. These results suggest that the microstructure of the bl…
We study thermodynamical properties of static dyonic AdS black holes in four-dimensional $ω$-deformed Kaluza-Klein gauged supergravity theory, and find that the differential first law requires a modification via introducing a new pair of thermodynamical conjugate variables (X, Y). To ensure such a modification, we then apply the quasi-local ADT formalism developed in Ref. [20] to calculate the quasi-local conserved charge and identify that the new pair is precisely the one previously introduced to modify the differential form of first law.
We construct a new class of vacuum black hole solutions whose geometry is deformed and twisted by the presence of NUT charges. The solutions are obtained by `unspinning' the general Kerr-NUT-(A)dS spacetimes, effectively switching off some of their rotation parameters. The resulting geometry has a structure of warped space with the Kerr-like Lorentzian part warped to a Euclidean metric of deformed and/or twisted sphere, with the deformation and twist characterized by the `Euclidean NUT' parameters. In the absence of NUTs, the solution reduces to a well known Kerr-(A)dS black hole with several …
Recently, two kinds of deformed schwarzschild spacetime have been proposed, which are the black-bounces metric (\cite{2019JCAP...02..042S,2021PhRvD.103h4052L}) and quantum deformed black hole (BH) (\cite{2021arXiv210202471B}). In present work, we investigate the rotating spacetime of these deformed Schwarzschild metric. They are exact solutions to the Einstein$'$s field equation. We analyzed the properties of these rotating spacetimes, such as event horizon (EH), stationary limit surface (SIS), structure of singularity ring, energy condition (EC), etc., and found that these rotating spacetime …
A new class of black hole solutions of the five dimensional minimal gauged supergravity is presented. They are characterized by the mass, the electric charge, two equal magnitude angular momenta and the magnitude of the magnetic potential at infinity. These black holes possess a horizon of spherical topology; however, both the horizon and the sphere at infinity can be arbitrarily squashed, with nonextremal solutions interpolating between black strings and black branes. A particular set of extremal configurations corresponds to a new one-parameter family of supersymmetric black holes. While the…
We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the resolution of the singularity of the black hole and a minimum nonzero radius for the infalling 2-spheres, provided that the deformation parameters are chosen to be negative.
We construct numerically static non-uniform black string solutions in six dimensions by using pseudo-spectral methods. An appropriately designed adaptation of the methods in regard of the specific behaviour of the field quantities in the vicinity of our numerical boundaries provides us with extremely accurate results, that allows us to get solutions with an unprecedented deformation of the black string horizon. Consequently, we are able to investigate in detail a critical regime within a suitable parameter diagram. In particular, we observe a clearly pronounced maximum in the mass curve, which…
We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant lambda. For lambda=1, the black hole resembles the Reissner-Norstrom black hole with a geometric parameter acting like the electric charge. Therefore, we obtain some differences in the entropy when comparing with the Schwarzschild black hole. Finally, we study the heat capacity and the thermodynamical stability of this solution.
We study a higher order conformally coupled scalar tensor theory endowed with a covariant geometric constraint relating the scalar curvature with the Gauss-Bonnet scalar. It is a particular Horndeski theory including a canonical kinetic term but without shift or parity symmetry for the scalar. The theory also stems from a Kaluza-Klein reduction of a well defined higher dimensional metric theory. Properties of an asymptotically flat spherically symmetric black hole are analyzed, and new slowly rotating and radiating extensions are found. Through disformal transformations of the static configura…
We consider a charged Lifshitz black hole in the large transverse dimension limit. In this setup, the dynamics near the black hole horizon are shown to be effectively governed by a family of two-dimensional models of dilaton gravity depending on the ratio of the dynamical parameter characterizing the black hole and the dimension of spacetime. This family includes the Callan-Giddings-Harvey-Strominger (CGHS) and Jackiw-Teitelboim (JT) models and their charged equivalents. This family also contains classes of asymptotically anti-de Sitter models beyond JT, characterized by a running Ricci scalar…
We consider a simple model of a black hole surrounded by a toroidal structure and experiencing deformation due to magnetic field and the tidal force. For this system we construct the shadows of Preston-Poisson black hole, apply it to supermassive black hole $M87^*$ and compare it with the shadows of corresponding Schwarzschild and Kerr black holes. We find that for large deviation parameters $B$ and $E$ the shadow of Preston-Poisson black hole is clearly distinguishable from Kerr black hole provided the angular resolution of measurements is of order $μ\mathrm{arcsec}$.
We consider the entanglement island in a deformed Jackiw-Teitelboim black hole in the presence of the phase transition. This black hole has the van der Waals-Maxwell-like phase structure as it is coupled with a Maxwell field. We study the behavior of the Page curve of this black hole by using the island paradigm. In the fixed charge ensemble, we discuss different situations with different charges that influence the system's phase structure. There is only a Hawking-Page phase transition in the absence of charges, which leads to an unstable small black hole. Hence, the related Page curve does no…
We study the second-order phase transition (SOPT) for the spherically symmetric Kehagias-Sfetsos (KS) black hole in the deformed Hǒrava-Lifshitz gravity by applying the methods of equilibrium and non-equilibrium fluctuations. We find that, although the KS black hole has only one mass parameter as the usual Schwarzschild ones, the SOPT will take place if the mass of the KS black hole changes across the critical point $\frac{\sqrt{5+\sqrt{33}}(\sqrt{33}-1)} {16\sqrtω} $. The result show us that there is difference between the Hǒrava-Lifshitz gravity and the Einstein's gravity theory.
We study the possible black string-black hole transition by analyzing the structure of the apparent horizon for a large family of time-symmetric initial data. We observe that, as judged by the apparent horizon, it is possible to generate arbitrarily deformed black strings at a moment of time symmetry. A similar study for hyperspherical black holes reveals that although arbitrarily deformed hyperspherical black holes can be constructed, the proper distance between the north and south poles along the extra direction has an upper limit.
Planck spectrum of black body radiation is usually derived by considering of quantized free electromagnetic field at a finite temperature. The minimum-length deformed quantization affects field theory both at the first and second quantization levels. Performing an exact calculation to the first order in deformation parameter, both of the corrections turn out to be of the same order. Nevertheless, the correction at the second quantization level has some qualitative difference, that may be interesting for future study to differentiate between these two sorts of corrections. In itself the correct…
Adopting the strong field limit approach, we studied the properties of strong field gravitational lensing in the deformed Hǒrava-Lifshitz black hole and obtained the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit. Comparing with the Reissner-Norstr\"{om} black hole, we find that with the increase of parameter $α$, the angular position $θ_{\infty}…
Black holes with planar or hyperbolic horizons are known to exist in AdS space, alongside the usual ones with spherical horizons. In this paper, we consider a one-parameter generalisation of these black holes that is contained in the AdS C-metric. In terms of the domain-structure analysis recently developed for such solutions, these black holes have a domain in the shape of a triangle. It is shown that the horizons of these black holes are deformed hyperbolic spaces, with the new parameter controlling the amount of deformation. The space-times are static and completely regular outside the hori…
Institut für Theoretische Physik, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany（法兰克福理论物理研究所）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan（京都大学引力物理与量子信息中心、汤川理论物理研究所）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan（东京大学理学研究宇宙早期研究中心（RESCEU））；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan（东京大学宇宙物质科学 Kavli 研究所（WPI））；Departamento de Física, Universidad del País Vasco UPV/EHU, Apartado 644, 48080 Bilbao, Spain（巴斯克大学物理系）；EHU Quantum Center, Universidad del País Vasco UPV/EHU（巴斯克大学 EHU 量子中心）
In the present work the approach - density matrix deformation - earlier developed by the author to study a quantum theory of the Early Universe (Planck's scales) is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibility for application of the proposed approach to the calculation of quantum entropy of a black hole is considered.
In this paper, we investigate so-called spherical photon orbits around a deformed Kerr black hole with an extra deformation parameter. The change in the azimuth $Δφ$ and the angle of dragging of nodes per revolution $ΔΩ$ of a complete latitudinal oscillated orbit is calculated analytically. Finally, representative six examples orbits are plotted out to illustrate how spherical photon orbits look like and exhibit some interesting behavior. Especially, this spherical photon orbits are absent in circular orbits and different from the Kerr case.
In previous works, we have developed an approach to fix the leading behaviors of the pure AdS$_3$ and BTZ black hole from the entanglement entropies of the free CFT$_2$ and finite temperature CFT$_2$, respectively. We exclusively use holographic principle only and make no restriction about the bulk geometry, not only the kinematics but also the dynamics. In order to verify the universality and correctness of our method, in this paper, we apply it to the $T\bar{T}$ deformed CFT$_2$, which breaks the conformal symmetry. In terms of the physical arguments of the $T\bar{T}$ deformed CFT$_2$, the d…
We study the accretion process in the thin disk around a rotating non-Kerr black hole with a deformed parameter and an unbound rotation parameter. Our results show that the presence of the deformed parameter $ε$ modifies the standard properties of the disk. For the case in which the black hole is more oblate than a Kerr black hole, the larger deviation leads to the smaller energy flux, the lower radiation temperature and the fainter spectra luminosity in the disk. For the black hole with positive deformed parameter, we find that the effect of the deformed parameter on the disk becomes more com…
Alternative theories of gravity and the parameterized deviation approach allow black hole solutions to have additional parameters beyond mass, charge and angular momentum. Matter fields could be, in principle, affected by the additional parameters of these solutions. We compute the absorption cross section of massless spin-0 waves by static Konoplya-Zhidenko black holes, characterized by a deformation parameter introduced in the mass term, and compare it with the well-known absorption of a Schwarzschild black hole with the same mass. We compare our numerical results with the sinc approximation…
We first briefly revisit the original Hamilton-Jacobi method and show that the Hamilton-Jacobi equation for the action $I$ of tunnelings of a fermionic particle from a charged black hole can be written in the same form as that of a scalar particle. For the low energy quantum gravity effective models which respect covariance of the curved spacetime, we derive the deformed model-independent KG/Dirac and Hamilton-Jacobi equations using the methods of effective field theory. We then find that, to all orders of the effective theories, the deformed Hamilton-Jacobi equations can be obtained from the …
In this paper, we use the WKB approximation method to approximately solve a deformed Schrodinger-like differential equation: $\left[ -\hbar^{2} \partial_ξ^{2}g^{2}\left( -i\hbarα\partial_ξ\right) -p^{2}\left( ξ\right) \right] ψ\left( ξ\right) =0$, which are frequently dealt with in various effective models of quantum gravity, where the parameter $α$ characterizes effects of quantum gravity. For an arbitrary function $g\left( x\right) $ satisfying several properties proposed in the paper, we find the WKB solutions, the WKB connection formulas through a turning point, the deformed Bohr--Sommerfe…
Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full th…
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 …
Here we consider two phenomena in the vicinity of a black hole deformed by the tidal gravitational force of surrounding matter and by a strong magnetic field: equatorial motion of charged particles and the decay of a test scalar field. We were able to analyze both phenomena with analytical and simple numerical tools, which was unexpected given the low symmetry of the system. We show that both the tidal gravitational force and the magnetic field strongly enhance the release of the binding energy for the matter spiralling into the black hole. In the presence of the magnetic field, the left and r…
The geometric optics approximation provides an interpretation for eikonal correspondence that, in black-hole-containing spacetimes, connects high-frequency black hole quasinormal modes with closed photon orbits around said black hole. This correspondence has been identified explicitly for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes, the violation of which can be a potential hint toward physics beyond General Relativity. Notably, the aforementioned black hole spacetimes have sufficient symmetries such that both the geodesic equations and the master wave equations are se…
