Accurate correction of arbitrary spin fermions quantum tunneling from non-stationary Kerr-de Sitter black hole based on corrected Lorentz dispersion relation
Bei Sha, Zhi-E Liu, Yu-Zhen Liu, Xia Tan, Jie Zhang, Shu-Zheng Yang
According to a corrected dispersion relation proposed in the study on string theory and quantum gravity theory, Rarita-Schwinger equation has been precisely modified, which results in a Rarita-Schwinger-Hamilton-Jacobi equation, and through which, the characteristics of arbitrary spin fermions quantum tunneling radiation from non-stationary Kerr-de Sitter black hole are researched. A series of accurately corrected physical quantities such as surface gravity, chemical potential, tunneling probability and Hawking temperature that describe the properties of the black hole are derived. This research has enriched the research methods and made precision of the research contents of black hole physics.
We study the family of Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant. This leads to a quantisation condition on the masses and charges of the resulting Euclidean solutions.
We find an exact solution of Kerr-Newman-de Sitter type on the braneworld(4D) of the DGP model. When a constant 4D Ricci scalar is assumed, only zero(flat) and a positive(de-Sitter) values satisfy the Hamiltonian constraint equation coming from the extra dimension. With a Z_2-symmetry across the brane and a stationary and axisymmetric metric ansatz on the brane, we solve the constraint equation exactly in the Kerr-Schild form with de-Sitter background. In the de-Sitter background this Kerr-Schild solution is well behaved under Boyer-Lindquist transformation: the constraint equation is preserve…
Generalising arXiv:1511.08496, we construct further families of compact Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant.
We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.
We show how to compute the mass of a Kerr-anti-de Sitter spacetime with respect to the anti-de Sitter background in any dimension, using a superpotential which has been derived from standard Noether identities. The calculation takes no account of the source of the curvature and confirms results obtained for black holes via the first law of thermodynamics.
We first calculate equations of motion for particles in the Kerr-Sen-de Sitter black hole spacetime. Then in the eikonal regime, we analytically obtain the quasi-normal resonant modes of massless neutral scalar field perturbation and find its imaginary part to be characterized by the surface gravity of the near-extremal Kerr-Sen-de Sitter black hole with Cauchy horizon approaching the event horizon. We further show that the Penrose strong cosmic censorship conjecture is thus respected in this spacetime with dilaton scalar field and axion pseudoscalar field.
In the context of the Hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of …
We use zero angular momentum null geodesics in the Kerr-de Sitter spacetime to transform the metric in a generalised Bondi coordinate system. We write the metric components explicitly. Next, we choose the radial coordinate to be the areal coordinate and write the asymptotic metric in the Bondi-Sachs gauge.
We consider Kerr-de Sitter spacetimes and evaluate their mass, angular momentum and entropy according to the boundary counterterm prescription. We provide a physicall interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr-de Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the entropic N-bound. Moreover, we show that maximal mass conjecture which states any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity is respected by asymptotically de …
We compute the mass and angular momenta of rotating anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from standard Noether identities. The calculation relies on the fact that the Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when linearized on maximally symmetric backgrounds and uses the recently discovered D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations.
We describe three-dimensional Kerr-de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2,C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein-Hawking entropy connected to the cosmological horizon of Kerr-de Sitter space.
Recently, Banãdos, Silk and West (BSW) found that the center-of-mass energy of two colliding test particles in the neighborhood of an extreme Kerr black hole could be arbitrarily high when one particle has the critical angular momentum $L_\text{C}$. In their paper, they considered the black holes living in a Minkowski space-time with a zero cosmological constant. In this work, we study this process of particles in the backgrounds of the Kerr black holes living in a space-time with a nonzero cosmological constant. We find that for kerr black holes living in a space-time with a negative cosmolog…
The quantum tunneling radiation of fermions with arbitrary spin at the event horizon of Kerr-de Sitter black hole is accurately modified by using the dispersion relation proposed in the study of string theory and quantum gravitational theory. The derived tunneling rate and temperature at the black hole horizons are analyzed and studied.
We investigate in detail the mechanism of superradiance to render the instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant. We also discuss the spontaneous scalarization in the de Sitter background and find that this instability can also happen in the spherical de Sitter configuration in a special style.
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
Different forms of the metric for the Kerr-NUT-(anti-)de Sitter space-time are being widely used in its extension to higher dimensions. The purpose of this note is to relate the parameters that are being used to the physical parameters (mass, rotation, NUT and cosmological constant) in the basic four dimensional situation.
Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.
It has been recently shown that magnetic reconnection can provide us a novel mechanism to extract black hole rotational energy from a Kerr black holes. In this paper, we study the energy extraction from the Kerr-de Sitter black hole via this magnetic reconnection process. The result shows that, with the increase of the cosmological constant, a slowly spinning Kerr-de Sitter black hole can implement the energy extraction better than its Kerr counterpart. Interestingly, although the numerical results show that the maximum values of the power and efficiency slightly decrease with the cosmological…
We study Killing horizons and their neighbourhoods in the Kerr-NUT-(anti-)de Sitter and the accelerated Kerr-NUT-(anti-)de Sitter spacetimes. The geometries of the horizons have an irremovable singularity at one of the poles, unless the parameters characterising the spacetimes satisfy the constraint we derive and solve in the current paper. In the Kerr-NUT-de Sitter case, the constraint relates the cosmological constant of spacetime and the horizon area, leaving 3 parameters free. In the accelerated case the acceleration becomes a 4th parameter that allows the cosmological constant to take arb…
We calculate the total flux of Hawking radiation from Kerr-(anti)de Sitter black holes by using gravitational anomaly method developed in gr-qc/0502074. We consider the general Kerr-(anti)de Sitter black holes in arbitrary $D$ dimensions with the maximal number [D/2] of independent rotating parameters. We find that the physics near the horizon can be described by an infinite collection of $(1+1)$-dimensional quantum fields coupled to a set of gauge fields with charges proportional to the azimuthal angular momentums $m_i$. With the requirement of anomaly cancellation and regularity at the horiz…
We discuss the quantum creation scenario of a Kerr-de Sitter black hole in all dimensions. We show that its relative creation probability is the exponential to the entropy of the black hole, using a topological argument. The action of the regular Euclidean instanton can be calculated in the same way.
We compute the conserved charges for Kerr anti-de Sitter spacetimes in various dimensions using the conformal and the counterterm prescriptions. We show that the conserved charge corresponding to the global timelike killing vector computed by the two methods differ by a constant dependent on the rotation parameter and cosmological constant in odd spacetime dimensions, whereas the charge corresponding to the rotational killing vector is the same in either approach. We comment on possible implications of our results to the AdS/CFT correspondence.
Scattering data can be generically described in terms of monodromies. Here we obtain scattering amplitudes for conformally coupled scalar fields in Kerr-de Sitter black holes using this monodromy technique. The only non-trivial parameter, the composite monodromy parameter $σ_{ij}$ between two regular singular points, can be solved implicitily in terms of the Painlevé VI $τ$-function. The application of the Virasoro conformal blocks to solve the latter can now be interpreted as a verification of the striking relationship between conformal symmetry and black holes.
We investigate the first law of thermodynamics in the case of the (2+1)-dimensional BTZ black holes and Kerr-de Sitter spacetimes, in particular, we focus on the integral mass formulas. It is found that by assuming the cosmological constant as a variable state parameter, both the differential and integral mass formulas of the first law of black hole thermodynamics in the asymptotic flat spacetimes can be directly extended to those of rotating black holes in anti-de Sitter and de Sitter backgrounds. It should be pointed that these formulas come into existence in any dimensions also.
We interpret the cosmological constant as the energy of the vacuum, and under a minimum amount of assumptions, we show that it is deformed in the vicinity of a black hole. This leads us to reexamine the Kerr-de Sitter solution. We provide a new solution, simpler and geometrically richer, which shows the impact of the rotation in form of a warped curvature. We carry out a detailed and exact study on the new black hole solution, and we conclude with a conjecture regarding the possible impact of our results on alternative theories.
We consider the quasilocal thermodynamics of rotating black holes in asymptotically flat and asymptotically anti de Sitter spacetimes. Using the minimal number of intrinsic boundary counterterms inspired by the AdS/CFT correspondence, we find that we are able to carry out an analysis of the thermodynamics of these black holes for virtually all possible values of the rotation parameter and cosmological constant that leave the quasilocal boundary well-defined, going well beyond what is possible with background subtraction methods. Specifically, we compute the quasilocal energy $E$ and angular mo…
The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have cohomogeneity 2, and they admit a generalisation in which an additional parameter characterising a NUT charge is included. In this paper, we study the higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by appropriate restrictions on their rotation parameters, and we show how they too admit a generalisation in which an additional NUT-type parameter is introduced. We discuss also the supersymmetric limits of the new metrics. If one performs a Wick rotation to Euclidean spacetime signature, these yield new E…
A quantum deformation of three-dimensional de Sitter space was proposed in hep-th/0407188. We use this to calculate the entropy of Kerr-de Sitter space, using a canonical ensemble, and find agreement with the semiclassical result.
The equation of cosmic string loops in Kerr-de Sitter spacetimes is derived. Having solved the equation numerically, we find that the loops can expand and exist except for too small ones.
We studied the correction of the quantum tunneling radiation of fermions with spin $1/2$ in Kerr Anti-de-Sitter black hole. First, the dynamic equation of spin $1/2$ fermions was corrected using Lorentz's violation theory. Second, the new expressions of the fermions quantum tunneling rate, the Hawking temperature of the black hole and the entropy of the black hole were obtained according to the corrected fermions dynamic equation. At last, some comments are made on the results of our work.
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 study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-de Sitter spacetime in all dimensions. Complete separation of both equations is carried out in 2n+1 spacetime dimensions with all n rotation parameters equal, in which case the rotational symmetry group is enlarged from (U(1))^n to U(n). We explicitly construct the additional Killing vectors associated with the enlarged symmetry group which permit separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.
We determine the most general solution of the five-dimensional vacuum Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor that is type II or more special in the classification of Coley et al., (ii) a non-degenerate "optical matrix" encoding the expansion, rotation and shear of the aligned null direction. The solution is specified by three parameters. It is locally isometric to the 5d Kerr-de Sitter solution, or related to this solution by analytic continuation or taking a limit. This is in contrast with four dimensions, where there exist infinitely many solutions wi…
In this article we present results for tensor graviton modes (in seven dimensions and greater, $n\geq 3$) for greybody factors of Kerr-dS black holes and for Hawking radiation from simply rotating (n+4)-dimensional Kerr black holes. Although there is some subtlety with defining the Hawking temperature of a Kerr-dS black hole, we present some preliminary results for emissions assuming the standard Hawking normalization and a Bousso-Hawking-like normalization.
Incorporating Parikh and Wilczek's opinion to the Kerr de-Sitter (KdS) black hole Hawking non-thermal and purely thermal radiations have been investigated using Hamilton-Jacobi method. We have taken the background spacetime of KdS black hole as dynamical, involving the self-gravitation effect of the emitted particles, energy and angular momentum has been taken as conserved and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum. The explored results gives a correction to the Hawking radiat…
We study spacetimes with a closed conformal Killing-Yano tensor. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu-Pope is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor with a certain symmetry.
Quasinormal modes of scalar, electromagnetic, and gravitational fields in the extreme Schwarzschild-de Sitter background are known to be expressed in analytic form as eigenvalues of the Pöschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the Pöschl-Teller effective potential. Nevertheless, using the Frobenius method we find quasinormal modes analytically in this case as well. We write down the analytical formula for quasinormal frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is…
Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study the separability of gravitational perturbations in the generalized Kerr-NUT-de Sitter spacetime. We show that a certain type of tensor perturbations admits the separation of variables. The linearized perturbation equations for the Einstein condition are transformed into the ordinary differential equations of Fuchs type.
We study false vacuum decay in a black hole (BH) spacetime with an angular momentum. Considering the false vacuum region described by a Kerr-de Sitter geometry, under the thin wall approximation, we can obtain the stationary configuration of the vacuum bubble seen from the outside false vacuum region without specifying the geometry inside the domain wall. Then, assuming the true vacuum region is described by a Kerr geometry, we can fix the mass and the spin parameter for the Kerr geometry by imposing the 1st junction conditions and conservation of the angular momentum. Although the assumption …
The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equall…
In this paper, we consider the rotating charged Gödel black hole and study the effect of the higher order corrections of the entropy on the thermodynamics and statistics quantities of the Kerr-Newman-Gödel black hole. The leading order correction is logarithmic while higher-order terms are proportional to the inverse of the area of the black hole. We obtain modified thermodynamics and statistics and find that correction terms are important in the stability of the black hole.
We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The Kerr-de Sitter space describes the gravitational background of a point particle whose mass and spin are given by $1-M$ and $J$ and its curvature radius is given by $\ell$. In order to study the propagation of metric, dilaton, and Kalb-Ramond two-form, we perform the perturbation analysis in the southern diamond of Kerr-de Sitter space including a conical singularity. It reveals a mixing between the dilaton and other unphys…
We explicitly calculate the Riemannian curvature of D-dimensional metrics recently discussed by Chen, Lu and Pope. We find that they can be concisely written by using a single function. The Einstein condition which corresponds to the Kerr-NUT-de Sitter metric is clarified for all dimensions. It is shown that the metrics are of type D.
We have investigated spin interaction under the collision of Kerr-(anti-)de Sitter black holes. The potential of a spin interaction is dependent on the relative rotating directions of the black holes, and this potential can be released as gravitational radiation under the collision. The radiation depends on the cosmological constant and corresponds to the potential of the spin interaction at a limit where one of the black holes is assumed to have small mass and angular momentum. Then, we have shown, approximately, the overall behaviors of the upper bounds on the radiation using thermodynamics.…
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only s…
This note addresses quasinormal mode frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky's equations for Kerr-de Sitter black holes are mapped to Heun's equations, we are able to compute their quasinormal mode frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating bla…
Spatially homogeneous cosmological spacetimes, evolving in the presence of a positive cosmological constant and matter satisfying some reasonable energy conditions, typically approach the de Sitter geometry asymptotically (at least locally). In this work, we propose an alternate way to characterize this phenomena. We focus on a subset of such models admitting a generalized Kerr-Schild representation. We argue that the functions which define such a representation can be chosen, such that, their asymptotic behavior make the evolution towards the de Sitter spacetime manifest through the represent…
We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D\ge 4, with the maximal number [(D-1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter metric plus the square of a null geodesic vector, and in generalised Boyer-Lindquist coordinates. The Kerr-Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D\le 11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and are…
Based on the entropy function formalism, we consider the extremal Kerr-(anti-)de Sitter black holes in 4-dimensions. Solving differential equations exactly, which are obtained by extremizing the entropy function, we find agreement of the result with Bekenstein-Hawking entropy. Concerning the higher derivative corrections, we extend the computation to the case with Gauss-Bonnet term.
We construct a general class of non-extremal charged Kerr-de Sitter black holes in five dimensions, in which the two rotation parameters are set equal. There are three non-trivial parameters, namely the mass, charge and angular momentum. All previously-known cases, supersymmetric and non-supersymmetric, that have equal angular momenta are encompassed as special cases.
It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr-(anti-)de Sitter black hole with two independent angular momenta. A first order symmetry operator that commutes with the Dirac operator is constructed in terms of a rank-three Killing-Yano tensor whose square is a second order symmetric Stackel-Killing tensor admitted by the five-dimensional Kerr-(anti-)de Sitter spacetime. We highlight the construction procedure of such a symmetry operator. In addition, the first law of black hole thermodynamics has been extended to the case that the cosmological…
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…
