Kerr Newman De Sitter Research Articles

Analysis of high-frequency limit in absorption cross-section for Kerr–Newman–de Sitter black hole

In this paper, we study the critical impact parameter and Lyapunov exponent for a massive charged particle and a photon in the Kerr–Newman–de Sitter (KNdS) spacetime. From the geodesic equations obtained for the particle traveling parallel to the rotation axis (on-axis) of the KNdS spacetime and using the complex angular momentum (CAM) technique, it is found that the total absorption cross-section at a high-frequency limit oscillates with decreasing amplitude. We show that the black hole charge and spin affect the total absorption cross-section in the case of both the massive charged particle and photon.

Regularity of a double null coordinate system for Kerr–Newman–de Sitter spacetimes

AbstractWe construct a double null coordinate system $$(u,v,\theta _\star ,\phi _\star )$$ ( u , v , θ ⋆ , ϕ ⋆ ) for Kerr–Newman–de Sitter black hole interior spacetimes and prove that the two dimensional spheres given by the intersection of the hypersurfaces $$u=\hbox {constant}$$ u = constant and $$v=\hbox {constant}$$ v = constant are $$C^\infty$$ C ∞ in Boyer–Lindquist coordinates (including at the “poles"). The null coordinates allow one to immediately extend some results previously proven for Kerr. As an example, we illustrate how Sbierski’s result in (On the initial value problem in general relativity and wave propagation in black-hole spacetimes. Doctoral thesis, 2014. https://doi.org/10.17863/CAM.16140), for the wave equation on the black hole interior, for Reissner–Nordström and Kerr spacetimes, applies to Kerr–Newman–de Sitter spacetimes.

Constrained spin systems and KNdS black holes

Kerr-Newman de Sitter (KNdS) spacetimes have a rich thermodynamic structure that involves multiple horizons, and so differs in key respects from asymptotically flat or AdS black holes. In this paper, we show that certain features of KNdS spacetimes can be reproduced by a constrained system of N non-interacting spins in a magnetic field. Both the KNdS and spin systems have bounded energy and entropy, a maximum of the entropy in the interior of the energy range, and a symmetry that maps lower energy states to higher energy states with the same entropy. Consequently, both systems have a temperature that can be positive or negative, where the gravitational temperature is defined analogously to that of the spins. We find that the number of spins N corresponds to 1/Λ for black holes with very small charge q and rotation parameter a, and scales like a2+q2/Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\left({a}^2+{q}^2\\right)/\\Lambda} $$\\end{document} for larger values of a and q. These comparisons show that certain key features of the complex thermodynamics of KNdS spacetimes are reproduced by a simple system of noninteracting spins, suggesting that there may be a relatively simple effective description of quantum de Sitter black holes in terms of a finite dimensional Hilbert space.

Quantum absorption properties of Kerr–Newman–de Sitter black hole

In this work, we utilize the Wentzel–Kramers–Brillouin (WKB) approximation to determine the Hawking temperature corresponding to the Kerr–Newman–de Sitter (KNdS) spacetime. Specifically, we calculate the low frequency absorption cross-section for the KNdS black hole in a charged scalar field and analyzed its dependence on the characteristics of the black hole. Through our research, we have established a correlation between the absorption cross-section ([Formula: see text]) and the Hawking temperature ([Formula: see text]) of the black hole, demonstrating an inverse proportionality between the two quantities. Furthermore, we also deduce the absorption cross-sections for Kerr–de Sitter, Reissner–Nordstrom–de Sitter, Schwarzschild–de Sitter and Schwarzschild black holes, and compare them with previously obtained results. The validity of our findings is demonstrated by these comparisons.

Fermions tunneling of Kerr–Newman–de Sitter black hole in Lorentz violation theory

In this paper, the tunneling of fermions near the event horizon of Kerr–Newman–de Sitter (KNdS) black hole is investigated in frame dragging coordinate systems, Eddington coordinate system and Painleve coordinate system by using Dirac equation with Lorentz violation theory, Feynman prescription and WKB approximation. The Hawking temperature, heat capacity and change in black hole entropy of the black hole are modified due to the presence of Lorentz violation theory. The modified Hawking temperatures, heat capacities and change in black hole entropies at the event horizon of KNdS black hole would increase or decrease depending upon the choices of ether like vectors [Formula: see text]. In the absence of Lorentz violation theory, the original Hawking temperature, entropy and heat capacity are recovered.

Motion equations in a Kerr–Newman–de Sitter spacetime: some methods of integration and application to black holes shadowing in Scilab

In this paper, we recall some basic facts about the Kerr–Newman–(anti) de Sitter (KNdS) spacetime and review several formulations and integration methods for the geodesic equation of a test particle in such a spacetime. In particular, we introduce some basic general symplectic integrators in the Hamiltonian formalism and we re-derive the separated motion equations using Carter’s method. After this theoretical background, we explain how to ray-trace a KNdS black hole, equipped with a thin accretion disk, using Scilab. We compare the accuracy and execution time of the previous methods, concluding that the Carter equations is the best one. Then, inspired by Hagihara, we apply Weierstrass’ elliptic functions to the non-rotating case, yielding a fairly fast shadowing program for such a spacetime. We provide some illustrations of the code, including a depiction of the effects of the cosmological constant on shadows and accretion disk, as well as a simulation of M87*.

Hawking radiation of charged massive particle and tunneling from Kerr–Newman–de Sitter black hole

The semiclassical tunneling technique proposed by Parikh and Wilczek to study Hawking radiation of static and stationary black holes has been extensively used to investigate the Hawking radiation of different types of black holes. In this paper, the geodesic equation of charged massive particle and the massless particle are obtained by using the Lagrangian analysis. The geodesic equations of charged massive particle and massless particle are determined uniformly and consistently. Based on the geodesic equation, the Hawking radiation of the charged massive particle is investigated near the event horizon of Kerr–Newman–de Sitter black hole. By finding the imaginary part of the action of charged massive particle, the Hawking temperature and the tunneling probability of charged massive particle across the event horizon of KNdS black hole are obtained. The finding of this paper is a development for Parikh–Wilczek’s tunneling technique.

Analytic formula for quasinormal modes in the near-extreme Kerr-Newman–de Sitter spacetime governed by a non-Pöschl-Teller potential

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 P\"oschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the P\"oschl-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 valid for both bosonic and fermionic fields. We further extend the analysis to the case of charged rotating black holes and find a general analytical formula for quasinormal modes of the fields of various spin for the near extreme Kerr-Newman-de Sitter spacetime.

Exact solution for wave scattering from black holes: Formulation

AbstractWe establish an exact formulation for wave scattering of a massless field with spin and charge by a Kerr–Newman–de Sitter black hole. Our formulation is based on the exact solution of the Teukolsky equation in terms of the local Heun function, and does not require any approximation. It serves as simple exact formulae with arbitrary high precision, which realize fast calculation without restrictions on model parameters. We highlight several applications including quasinormal modes, cross section, reflection/absorption rate, and Green function.

Modified Hawking radiation of stationary and nonstationary Kerr–Newman–de Sitter black hole

In this paper, the tunneling of vector boson particles across the event horizon of Kerr-Newman-de Sitter (KNdS) black hole is investigated using the WKB approximation and Hamilton-Jacobi ansatz to Proca equation. The tunneling probability and radiation spectrum at the event horizon of KNdS black hole is obtained. The modified Hawking radiation of stationary and non-stationary KNdS black hole are also investigated using the Rarita-Schwinger ansatz to the deformed Hamilton-Jacobi method and new tortoise coordinate transformation. It is observed that the modified Hawking temperatures near the event horizon for both stationary and nonstationary space times are dependent on the black hole parameters.

The radial Teukolsky equation for Kerr–Newman–de Sitter geometry: revisited

We use Heun-type solutions given in Suzuki et al. (Prog Theor Phys 100:491, 1998) for the radial Teukolsky equation written in the background metric of the Kerr–Newman–de Sitter geometry to calculate reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.

Hawking Radiations of Kerr-Newman Black Hole in de Sitter Spacetime by Hamilton-Jacobi Method

Incorporating Parikh and Wilczek’s opinion Hawking radiations of Kerr-Newman-de Sitter (KNdS) black hole has been investigated by Hamilton-Jacobi method. We have assumed the space time background as dynamical, energy and angular momentum as conserved incorporating the self-gravitation effect of the emitted particles. We have shown that the massive particle tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum.

Extension Rules of Newman–Janis Algorithm for Rotation Metrics in General Relativity

Aims: The aim of this study is to extend the formula of Newman–Janis algorithm (NJA) and introduce the rules of the complexifying seed metric. The extension of NJA can help determine more generalized axisymmetric solutions in general relativity.Methodology: We perform the extended NJA in two parts: the tensor structure and the seed metric function. Regarding the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically equivalent; however, the latter is more concise. Regarding the seed metric function, we propose the extended rules of a complex transformation by r2/Σ and combine the mass, charge, and cosmologic constant into a polynomial function of r.
 Results: We obtain a family of axisymmetric exact solutions to Einstein’s field equations, including the Kerr metric, Kerr–Newman metric, rotating–de Sitter, rotating Hayward metric, Kerr–de Sitter metric and Kerr–Newman–de Sitter metric. All the above solutions are embedded in ellipsoid- symmetric spacetime, and the energy-momentum tensors of all the above metrics satisfy the energy conservation equations.
 Conclusion: The extension rules of the NJA in this research avoid ambiguity during complexifying the transformation and successfully generate a family of axisymmetric exact solutions to Einsteins field equations in general relativity, which deserves further study.

The massive Dirac equation in the Kerr-Newman-de Sitter and Kerr-Newman black hole spacetimes

Exact solutions of the Dirac general relativistic equation that describe the dynamics of a massive, electrically charged particle with half-integer spin in the curved spacetime geometry of an electrically charged, rotating Kerr-Newman-(anti) de Sitter black hole are investigated. We first, derive the Dirac equation in the Kerr-Newman-de Sitter (KNdS) black hole background using a generalised Kinnersley null tetrad in the Newman-Penrose formalism. Subsequently in this frame and in the KNdS black hole spacetime, we prove the separation of the Dirac equation into ordinary differential equations for the radial and angular parts. Under specific transformations of the independent and dependent variables we prove that the transformed radial equation for a massive charged spin fermion in the background KNdS black hole constitutes a highly non-trivial generalisation of Heun’s equation since it possess five regular finite singular points. Using a Regge-Wheeler-like independent variable we transform the radial equation in the KNdS background into a Schrödinger like differential equation and investigate its asymptotic behaviour near the event and cosmological horizons. For the case of a massive fermion in the background of a Kerr-Newman (KN) black hole we first prove that the radial and angular equations that result from the separation of Dirac’s equation reduce to the generalised Heun differential equation (GHE). The local solutions of such GHE are derived and can be described by holomorphic functions whose power series coefficients are determined by a four-term recurrence relation. In addition using asymptotic analysis we derive the solutions for the massive fermion far away from the KN black hole and the solutions near the event horizon . The determination of the separation constant as an eigenvalue problem in the KN background is investigated. Using the aforementioned four-term recursion formula we prove that in the non-extreme KN geometry there are no bound states with , where ω and μ are the energy and mass of the fermion respectively.

Quantization of Horizon Area of Kerr–Newman–de Sitter Black Hole**Supported by the CSIR, Visiting Associate in Inter University Centre for Astronomy and Astrophysics, Pune, India

Using the adiabatic invariant action and applying the Bohr–Sommerfeld quantization rule and first law of black hole thermodynamics, a study of the quantization of the entropy and horizon area of a Kerr–Newman–de Sitter black hole is carried out. The same entropy spectrum is obtained in two different coordinate systems. It is also observed that the spacing of the entropy spectrum is independent of the black hole parameters. Also, the corresponding quantum of horizon area is in agreement with the results of Bekenstein.

Thermodynamics and Cosmic Censorship Conjecture in Kerr-Newman-de Sitter Black Hole.

We investigate the laws of thermodynamics and the validity of the cosmic censorship conjecture in the Kerr–Newman–de Sitter black hole under charged particle absorption. Here, the black hole undergoes infinitesimal changes because of the momenta carried by the particle entering it. The cosmic censorship conjecture is tested by whether the black hole can be overcharged beyond the extremal condition under absorption. The changes in the black hole violate the second law of thermodynamics. Furthermore, this is related to the cosmic censorship conjecture. To resolve this violation, we impose a reference energy of the particle at the asymptotic region based on the first law of thermodynamics. Under imposition of the reference energy, the absorption satisfies the laws of thermodynamics, and the extremal black hole cannot be overcharged. Thus, the cosmic censorship conjecture is valid under the absorption.

Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ > 0

We consider the wave equation on Reissner–Nordström–de Sitter and more generally Kerr–Newman–de Sitter black hole spacetimes with . The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes has been the subject of much discussion, since—in contrast to the asymptotically flat case—the competition with the decay associated to the region between the event and cosmological horizons is delicate, especially as the extremal limit is approached. Of particular interest is the question as to whether generic, admissible initial data posed on a Cauchy surface lead to solutions whose local (integrated) energy blows up at the Cauchy horizon, for this statement holds in the asymptotically flat case and would correspond precisely to the blow up required by Christodoulou’s formulation of strong cosmic censorship. Some recent heuristic work suggests that the answer is in general negative for solutions arising from sufficiently smooth data, i.e. there exists a certain range of black hole parameters such that for all such data, the arising solutions have finite local (integrated) energy at the Cauchy horizon. In this short note, we shall show in contrast that, by slightly relaxing the smoothness assumption on initial data, we are able to prove the analogue of the Christodoulou statement in the affirmative, i.e. we show that for generic data in our allowed class, the local energy blow-up statement indeed holds at the Cauchy horizon, for all subextremal black hole parameter ranges. We present two distinct proofs. The first is based on an explicit mode construction while the other is softer and uses only time translation invariance of appropriate scattering maps, in analogy with our previous (Dafermos and Shlapentokh-Rothman 2017 Commun. Math. Phys. 350 985–1016). Both proofs use statements concerning the non-triviality of transmission and reflexion, which are easy to infer by o.d.e. techniques and analyticity considerations. Our slightly enlarged class of initial data is still sufficiently regular to ensure both stability and decay properties in the region between the event and cosmological horizons as well as the boundedness and continuous extendibility beyond the Cauchy horizon. This suggests thus that it is finally this class—and not smoother data—which may provide the correct setting to formulate the genericity condition in strong cosmic censorship.

Quasi-normal modes for Dirac fields in the Kerr–Newman–de Sitter black holes

We provide the full asymptotic description of the quasi-normal modes (resonances) in any strip of fixed width for Dirac fields in slowly rotating Kerr–Newman–de Sitter black holes. The resonances split in a way similar to the Zeeman effect. The method is based on the extension to Dirac operators of techniques applied by Dyatlov in [Quasi-normal modes and exponential energy decay for the Kerr–de Sitter black hole, Commun. Math. Phys. 306(1) (2011) 119–163; Asymptotic distribution of quasi-normal modes for Kerr–de Sitter black holes, Ann. Henri Poincaré 13(5) (2012) 1101–1166] to the (uncharged) Kerr–de Sitter black holes. We show that the mass of the Dirac field does not have an effect on the two leading terms in the expansions of resonances. We give an expansion of the solution of the evolution equation for the Dirac fields in the outer region of the slowly rotating Kerr–Newman–de Sitter black hole which implies the exponential decay of the local energy. Moreover, using the [Formula: see text]-normal hyperbolicity of the trapped set and applying the techniques from [Asymptotics of linear waves and resonances with applications to black holes, Commun. Math. Phys. 335 (2015) 1445–1485; Resonance projectors and asymptotics for [Formula: see text]-normally hyperbolic trapped sets, J. Amer. Math. Soc. 28 (2015) 311–381], we give location of the resonance free band and the Weyl-type formula for the resonances in the band near the real axis.

Non-linear Stability of the Kerr–Newman–de Sitter Family of Charged Black Holes

We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a neighborhood of the exterior region of the black hole, the metric and the electromagnetic field decay exponentially fast to their values for a possibly different member of the KNdS family. This is a continuation of recent work of the author with Vasy on the stability of the Kerr-de Sitter family for the Einstein vacuum equations. Our non-linear iteration scheme automatically finds the final black hole parameters as well as the gauge in which the global solution exists; we work in a generalized wave coordinate/Lorenz gauge, with gauge source functions lying in a suitable finite-dimensional space. We include a self-contained proof of the linear mode stability of Reissner-Nordstr\"om-de Sitter black holes, building on work by Kodama-Ishibashi. In the course of our non-linear stability argument, we also obtain the first proof of the linear (mode) stability of slowly rotating KNdS black holes using robust perturbative techniques.

Quasinormal modes and strong cosmic censorship in near-extremal Kerr–Newman–de Sitter black-hole spacetimes

The quasinormal resonant modes of massless neutral fields in near-extremal Kerr–Newman–de Sitter black-hole spacetimes are calculated in the eikonal regime. It is explicitly proved that, in the angular momentum regime a¯>1−2Λ¯4+Λ¯/3, the black-hole spacetimes are characterized by slowly decaying resonant modes which are described by the compact formula ℑω(n)=κ+⋅(n+12) [here the physical parameters {a¯,κ+,Λ¯,n} are respectively the dimensionless angular momentum of the black hole, its characteristic surface gravity, the dimensionless cosmological constant of the spacetime, and the integer resonance parameter]. Our results support the validity of the Penrose strong cosmic censorship conjecture in these black-hole spacetimes.