Valentin D. Gladush, Alexander I. Petrusenko
The oscillations of the test particles on circular orbits in field of super-extremal charged central object are researched. The formulae for oscillation frequencies are obtained in cases of circular orbits perturbations caused by small change in energy of the particle or by the small change in mass of the central object.
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The superradiant stability is investigated for non-extremal Reissner-Nordstrom black hole. We use an algebraic method to demonstrate that all non-extremal Reissner-Nordstrom black holes are superradiantly stable against a charged massive scalar perturbation. This improves the results obtained before for non-extremal Reissner-Nordstrom black holes.
The superradiant stability of higher dimensional non-extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is analytically studied. We extend an analytical method developed by one of the authors in the extremal Reissner-Nordstrom black hole cases to non-extremal cases. Using the new analytical method, we revisit four-dimensional Reissner-Nordstrom black hole case and obtain that four-dimensional Reissner-Nordstrom black hole is superradiantly stable, which is consistent with results in previous works. We then analytically prove that the five-dimensional Reissner-Nor…
The Reissner-Nordström black hole - moving mirror correspondence is solved. The beta coefficients reveal that charge makes a black hole radiate fewer particles (neutral massless scalars) per frequency. An old Reissner-Nordström black hole emits particles in an explicit Planck distribution with temperature corresponding to the surface gravity of its outer horizon.
The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS black hole background is investigated. The essential self-adjointness of the Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is carried out in analogy with the standard Reissner-Nordstrom black hole case.
We calculate the electrostatic potential generated by a point charge in the space-time of Reissner-Nordstrom with a conical defect. An expression for the self-energy is also presented.
In this paper, we solve the massive scalar field in the Reissner-Nordström spacetime. The scalar field in the Reissner-Nordström spacetime has both bound states and scattering states. For bound states, we solve the bound-state wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the Reissner-Nordström spacetime.
We examine embedding diagrams of hypersurfaces in the Reissner-Nordstrom black hole spacetime. These embedding diagrams serve as useful tools to visualize the geometry of the hypersurfaces and of the whole spacetime in general.
We show that the tetrad field whose metric gives the Reissner-Nordström anti-de Sitter black holes gives the correct value of energy in Møller tetrad theory of gravitation.
The superradiant stability of asymptotically flat D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is analytically studied. Recently, an analytical method has been proposed by the author and used to prove that five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable under charged massive scalar perturbation. We apply this analytical method in the D-dimensional extremal Reissner-Nordstrom black hole cases and prove that the D-dimensional Reissner-Nordstrom black holes are all superradiantly stable under charged mas…
It was pointed out by Couch and Torrence that the extreme Reissner-Nordstrom solution possesses a discrete conformal isometry. Using results of Romans, it is shown that such a symmetry also exists when a non-zero cosmological constant is allowed.
In this work we study the trajectories of test particles in a geometry that is the nonlinear electromagnetic generalization of the Reissner-Nordstrom solution. The studied spacetime is a Einstein-Born-Infeld solution, nonsingular outside a regular event horizon and characterized by three parameters: mass $M$, charge $Q$ and the Born-Infeld parameter $b$ related to the magnitude of the electric field at the origin. Asymptotically it is a Reissner-Nordstrom solution
The scattering problems arising when considering the contribution of the topologically inequivalent configurations of the spinors on Reissner-Nordström black holes to the Hawking radiation are correctly stated. The corresponding $S$-matrices are described and presented in the form convenient to numerical computations.
We present a novel solution describing magnetized spacetime outside a massive object with electric charge equipped with NUT parameter. To get the solution, we employ the Ernst magnetization to the Reissner-Nordstrom-Taub-NUT spacetime as the seed. After discussing some physical aspects of the spacetime, we show that the extremal entropy of a magnetized Reissner-Nordstrom-Taub-NUT black hole can be reproduced by using the Cardy formula.
In this paper we consider some applications of the extended Dray-t'Hooft-Redmount relation. In particular, using this relation, we study geometries of interacting thin shells near the future Cauchy horizon of a Reissner-Nordstrom black hole.
The formalism developed by Chandrasekhar for the linear polar perturbations of the Reissner-Nordstrom solution is generalized to include the case of dipole (l=1) perturbations. Then, the perturbed metric coefficients and components of the Maxwell tensor are computed.
We solve numerically equations of motion for real self-interacting scalar fields in the background of Reissner-Nordstrom black hole and obtained a sequence of static axisymmetric solutions representing thick domain walls charged black hole systems. In the case of extremal Reissner-Nordstrom black hole solution we find that there is a parameter depending on the black hole mass and the width of the domain wall which constitutes the upper limit for the expulsion to occur.
We present the analytical post-Newtonian solutions for the test particle's motion in the Reissner-Nordström spacetime. The solutions are formulated in the Wagoner-Will representation, the Epstein-Haugan representation, the Brumberg representation, and the Damour-Deruelle representation, respectively. The relations between the (post-)Keplerian parameters in different representations, as well as their relations to the orbital energy and angular momentum are also provided.
The physical representation of the general double-Reissner-Nordstrom solution is obtained by rewriting the N=2 Breton-Manko-Aguilar electrostatic solution in the Varzugin-Chistyakov parametrization (M_i, Q_i, R). A concise analytical formula is derived for the interaction force between two arbitrary Reissner-Nordstrom constituents, and an example of the equilibrium configuration involving two oppositely charged particles which confirms earlier Bonnor's prediction of the existence of such configurations is given.
The superradiant stability of five and six-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is studied. In each case, it is analytically proved that the effective potential experienced by the scalar perturbation has only one maximum outside the black hole horizon and no potential well exists for the superradiance modes. So the five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable. In the proof, we develop a new method which is based on the Descartes' rule of signs for the polynomial equations. Our results general…
By using the gedanken experiments suggested by Bekenstein and Rosenzweig, we have shown that nonextremal Reissner-Nordstrom black hole cannot turn into extremal one by assimilating infalling charged particle and charged spherical shell.
We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordström space-time in terms of the Weierstraß $\wp$, $σ$ and $ζ$ elliptic functions. Based on the study of the polynomials in the $\vartheta$ and $r$ equations we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordström space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordström sp…
The superradiant stability of higher dimensional non-extremal Reissner-Nordstrom black hole under charged massive scalar perturbation is analytically studied. We extend our previous studies of four- and five-dimensional non-extremal Reissner-Nordstrom black hole cases to six-dimensional case. By analyzing the derivative of the effective potential with an analytical method, we find that no potential well exists outside the outer horizon of the black hole for the superradiant scalar modes. This means that there is no black hole bomb for the system consisting of six-dimensional Reissner-Nordstrom…
We find a new exact vacuum solution in the framework of the Poincaré Gauge field theory with massive torsion. In this model, torsion operates as an independent field and introduces corrections to the vacuum structure present in General Relativity. The new static and spherically symmetric configuration shows a Reissner-Nordström-like geometry characterized by a spin charge. It extends the known massless torsion solution to the massive case. The corresponding Reissner-Nordström-de Sitter solution is also compatible with a cosmological constant and additional U(1) gauge fields.
This note discusses the late-time decay of perturbations outside extremal Reissner-Nordstrom black hole. We consider individual spherical-harmonic modes $l$ of massless scalar field. The initial data are assumed to be of compact support, with generic regular behavior across the horizon. The scalar perturbations are found to decay at late time as $t^{-(2l+2)}$. We also provide the spatial dependence of the late-time tails, including the exact overall pre-factor.
An approach to computing, withing the framework of distribution theory, the distributional valued energy-momentum tensor for the Schwarzschild spacetime is disscused. This approach avoids the problems associated with the regularization of singularities in the curvature tensors and shares common features with the by now standard treatment of discontinuities in General Relativity. Finally, the Reissner-Nordstrom spacetime is also considered using the same approach.
Using Relativistic Quantum Geometry we show that the entropy can decrease in very small BHs, under certain circumstances, but always increases in very massive Black-Holes.
We perform a Hadamard point-split renormalization of the current density $j_ν$ of a charged scalar field in a Reissner-Nordström-de Sitter spacetime. We compute numerically the expectation values of the components $j_r$ and $j_t$ in the Unruh state in the exterior region and study their dependence on the field parameters and the position.
Spontaneous pair production near magnetized Reissner-Nordstrom black holes
本文研究了近极端磁化Reissner-Nordstrom黑洞附近的粒子对产生现象，将其解释为强场下的Schwinger效应，并通过数值示例展示了外部磁场增长与标量吸收之间的对应关系。
We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.
In this paper we propose a stationary solution of Einstein's field equations describing Reissner-Nordstrom black hole in dark energy background. It is to be regarded as the Reissner-Nordstrom black hole is embedded into the dark energy solution producing Reissner-Nordstrom-dark energy black hole. We find that the space-time geometry of Reissner-Nordstrom-dark energy solution is Petrov type $D$ in the classification of space-times. It is also shown that the embedded space-time possesses an energy-momentum tensor of the electromagnetic field interacting with the dark energy having negative press…
We investigate the existence of Reissner-Nordström (RN) type black holes in f(R) gravity. Our emphasis is to derive, in the presence of electrostatic source, the necessary conditions which provide such static, spherically symmetric (SSS) black holes available in f(R) gravity. We also study the thermodynamics of the black hole solution.
We study the linear metric perturbations of the Reissner-Nordström solution for the case of axial perturbation modes. We find that the well-known perturbative analysis fails for the case of dipole $(l=1)$ perturbations, although valid for higher multipoles. We define new radial functions, with which the perturbation formalism is generalized to all multipole orders, including the dipole. We then complete the solution by constructing the perturbed metric and Maxwell tensors.
This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0010068, gr-qc/9911018, gr-qc/0303034, and gr-qc/0212018.
In this paper, we construct the exact solutions of Reissner-Nordstrom black holes in the presence of quartic quasi-topological gravity. we obtain the thermodynamics and conserved quantities of the solutions and check the first law of thermodynamics. In studying the physical properties of the solutions, we consider asymptotically Ads, dS and flat solutions of Reissner-Nordstrom black hole in quartic quasi-topological gravity and compare them with Einstein and third-order quasi-topological gravities. we also investigate the thermal stability of the solutions that we show the thermal stability ar…
In this paper, we study by a functional method the vacuum instability of a charged scalar field, when it is quantized in the background of the Reissner-Nordtrom black hole; we also show that the first stage of the evaporation process of the black hole can be driven by a Schwinger-like effect.
The quasinormal resonance frequency of the higher-dimensional Reissner--Nordström (RN) black hole due to charged massive scalar field perturbation is deduced analytically in the eikonal regime. The characteristic decay timescale of the charged massive scalar perturbation in the background of the higher-dimensional RN spacetime is then obtained. The result reveals that longlived charged massive scalar field can exist in higher-dimensional RN spacetime under a certain condition.
The recent work of Nation et al in which Hawking radiation energy and entropy flow from a black hole can be regarded as a one-dimensional (1D) Landauer transport process is extended to the case of a Reissner-Nordstrom (RN) black hole. It is found that the flow of charge current can also be transported via a 1D quantum channel except the current of Hawking radiation. The maximum entropy current, which is shown to be particle statistics independence, is also obtained.
The scattering amplitudes for the perturbed fields of the N=2 supergravity about the extreme Reissner-Nordström black hole is examined. Owing to the fact that the extreme hole is a BPS state of the theory and preserves an unbroken global supersymmetry(N=1), the scattering amplitudes of the component fields should be related to each other. In this paper, we derive the formula of the transformation of the scattering amplitudes.
No black hole bomb for $D$-dimensional non-extremal Reissner-Nordstrom black holes against charged massive scalar perturbation
本文解析证明，任意维数（$D\geq7$）的非极端Reissner-Nordstrom黑洞在带电有质量标量微扰下均无超辐射不稳定，即不存在黑洞炸弹，推广了五维和六维的已知结论。
In this paper, we study the dynamical instability of gaseous sphere under radial oscillations approaching the Reissner-Nordström limit. For this purpose, we derive linearized perturbed equation of motion following the Eulerian and Lagrangian approaches. We formulate perturbed pressure in terms of adiabatic index by employing the conservation of baryon numbers. A variational principle is established to evaluate characteristic frequencies of oscillations which lead to the criteria for dynamical stability. The dynamical instability of homogeneous sphere as well as relativistic polytropes with dif…
We analyse various conformal properties of the extremal Reissner-Nordström spacetime. In particular, we obtain conformal representations of the neighbourhoods of spatial infinity, timelike infinity and the cylindrical end ---the so-called cylinders at spatial infinity and at the horizon, respectively--- which are regular with respect to the conformal Einstein field equations and their associated initial data sets. We discuss possible implications of these constructions for the propagation of test fields and non-linear perturbations of the gravitational field close to the horizon.
In this work we address the study of movement of charged particles in the background of charged black holes with non-trivial asymptotic behavior. We compute the exact trajectories for massive-charged particles in term of elliptic Jacobi function. Finally we obtain a detailed description of orbits for Reissner-Nordström (Anti)-de Sitter black holes in terms of charge, mass and energy of the particles.
We evaluate the complex frequencies of the normal modes for the massive charged scalar field perturbations around a Reissner-Nördstrom black hole surrounded by a static and spherically symmetric quintessence using third order WKB approximation approach. Due to the presence of quintessence, quasinormal frequencies damp more slowly. We studied the variation of quasinormal frequencies with charge of the black bole, mass and charge of perturbating scalar field and the quintessential state parameter.
In this paper we study the strong gravitational lensing scenario where the lens is a Reissner-Nordstrom black hole. We obtain the basic equations and show that, as in the case of Schwarzschild black hole, besides the primary and secondary images, two infinite sets of relativistic images are formed. We find analytical expressions for the positions and amplifications of the relativistic images. The formalism is applied to the case of a low-mass black hole placed at the galactic halo.
We describe twisted configurations of spinor field on the Schwarzschild and Reissner-Nordström black holes that arise due to existence of the twisted spinor bundles over the standard black hole topology. From a physical point of view the appearance of spinor twisted configurations is linked with the natural presence of Dirac monopoles that play the role of connections in the complex line bundles corresponding to the twisted spinor bundles. Possible application to the Hawking radiation is also outlined.
The behavior of a massive charged test Dirac field in the background of a Reissner-Nordström black hole is investigated. Especially, we obtain the frequencies of quasibound states by solving the Dirac equation numerically both in time and frequency domain. Our results suggest that although the absence of superradiance excludes the existence of stationary solutions for massive Dirac fields, it is still possible to find arbitrarily long-lived solutions.
We investigate the radiation emitted from a scalar source in circular orbit around a Reissner-Nordstrom black hole. Particle and energy emission rates are analytically calculated in the low- and high-frequency regimes and shown to be in full agreement with a numerical calculation. Our investigation is connected with the recent discussion on the validity of the cosmic censorship conjecture in the quantum realm.
Based on the generalized uncertainty principle, we study the entropy of a four-dimensional black hole by counting degrees of freedom near the horizon and obtain the (finite) entropy proportional to the surface area at the horizon without a cutoff introduced in the conventional brick-wall method.
A technique for extracting from the appropriate field equations the relativistic motion of Schwarzschild, Reissner-Nordstrom and Kerr particles moving in external fields is motivated and illustrated. The key assumptions are that (a) the particles are isolated and (b) near the particles the wave fronts of the radiation generated by their motion are smoothly deformed spheres. No divergent integrals arise in this approach. The particles are not test particles. The formalism is used, however, to derive the Mathisson-Papapetrou equations of motion of spinning test particles, neglecting spin-spin te…
The 3+1 spacetime formulation of general relativity is used to investigate the transverse waves propagating in a plasma influenced by the gravitational field of Reissner-Nordstrom black hole, as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here, a local approximation is used to investigate the one-dimensional radial propagation of longitudinal waves. We derive the dispersion relation for these waves and solve it numerically for the wave number k.
We compute characteristic (quasinormal) frequencies corresponding to decay of a massive charged scalar field in a Reissner-Nordstrom black hole background. It proves that, contrary to the behavior at very late times, at the stage of quasinormal ringing the neutral perturbations will damp slower than the charged ones. In the limit of the extremal black hole the damping rate of charged and neutral perturbations coincides. Possible connection of this with the critical collapse in a massive scalar electrodynamics is discussed.
Turnaround Radius for charged particles in the Reissner-Nordström deSitter spacetime
本研究分析了Reissner-Nordström de Sitter时空中带电测试粒子的转向半径，同时结合共形耦合引力的MTZ解考察标量测试电荷的情形，发现两类相互作用下转向半径均与粒子能量相关。
We derive the Teixeira, Wolk and Som method, for obtaining electrostatic solutions from given vacuum solutions, in its inverse form. Then we use it to obtain the geometrical mass $M_S$ in the Schwarzschild spacetime, and we find $M_S^2=M^2-Q^2$, where $M$ and $Q$ are, respectively, the mass and charge parameters of the Reissner-Nordström spacetime. We compare $M_S$ to the corresponding active gravitational mass and mass function.
In this paper, we study the existence of (quasi)bound states in two spacetime geometries describing Schwarzschild and Reissner-Nordström black holes. For obtaining this type of states we search for discrete quantum modes of the massive Dirac equation in the two geometries. After imposing the quantization condition, an analytical expression for the energy of the ground states is derived. The energy of higher states is then obtained numerically. For very small values of the black hole mass $M$ we compare the energy of the Reissner-Nordström black hole quasibound state with the Dirac-Coulomb ener…
We investigate dominant late-time tail behaviors of massive scalar fields in nearly extreme Reissner-Nordström background. It is shown that the oscillatory tail of the scalar fields has the decay rate of $t^{-5/6}$ at asymptotically late times. The physical mechanism by which the asymptotic $t^{-5/6}$ tail yields and the relation between the field mass and the time scale when the tail begins to dominate, are discussed in terms of resonance backscattering due to spacetime curvature.
The dynamics of a relativistic particle in a Reissner-Nordstrom background is studied using Caianiello model with maximal acceleration. The behaviour of the particle, embedded in a new effective geometry, changes with respect to the classical scenario because of the formation of repulsive potential barriers near the horizon. Black hole formation by accretion of massive particles is not therefore a viable process in the model. At the same time, the naked singularity remains largely unaffected by maximal acceleration corrections.
We consider the Brans-Dicke Reissner-Nordstrom spacetime in isotropic coordinates and the electrostatic field of an electric point charge placed outside its surface of inversion. We treat the static electric point charge as a linear perturbation on the Brans-Dicke Reissner-Nordstrom background. We develop a method based upon the Copson method to convert the governing Maxwell equation on the electrostatic potential generated by the static electric point charge into a solvable linear second order ordinary differential equation. We obtain a closed form fundamental solution of the curved space Lap…
We study a correct statement of the scattering problem arising for quantum charged scalar particles on the Reissner-Nordström black holes when taking into account the own electric field of black hole. The elements of the corresponding S-matrix are explored in the form convenient to physical applications and for applying numerical methods. Some further possible issues are outlined.
Studying particle motion in the gravitational field of a black hole from the perspective of different observers is important for separating the coordinate artifacts from the physical phenomena. In this paper, we show that a freely falling test particle exhibits gravitational repulsion by a black hole as seen by an asymptotic observer, whereas nothing of the kind happens as recorded by a freely falling observer or by an observer located at a finite distance from the event horizon. This analysis is carried out for a general Reissner-Nordström, an extremal Reissner-Nordström, and a Schwarzschild …
We quantize the low-energy sector of a massless scalar field in the Reissner-Nordstrom spacetime. This allows the analysis of processes involving soft scalar particles occurring outside charged black holes. In particular, we compute the response of a static scalar source interacting with Hawking radiation using the Unruh (and the Hartle-Hawking) vacuum. This response is compared with the one obtained when the source is uniformly accelerated in the usual vacuum of the Minkowski spacetime with the same proper acceleration. We show that both responses are in general different in opposition to the…
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