An analytic extension of the Reissner-Nordstrom solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at $r=0$. The metric is still singular in the new coordinates, but its components become finite and smooth. Using this extension it is shown that the charged and non-rotating black hole singularities are compatible with the global hyperbolicity and with the conservation of the initial value data. Geometric models for electrically charged particles are obtained.
We solve the spacelike, spherically symmetric, constant mean curvature hypersurfaces in the maximally extended Reissner-Nordstrom spacetime with the charge smaller than the mass. Based on these results, we construct constant mean curvature foliations with fixed or varied mean curvature in each slice in this spacetime.
In this work, the fermion behaviour near the Reissner-Nordstrom black holes in quantum mechanics is studied and exact solutions of the Dirac equation for Reissner-Nordstrom Black Holes are obtained in terms of special functions. We have obtained different vector potentials which satisfy the solutions.
It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordstrom black hole background; in particular, there are no static solutions of the Dirac equation in such a background field. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.
The electromagnetic field of the ultrarelativistic Reissner-Nordstrom solution shows the physically highly unsatisfactory property of a vanishing field tensor but a nonzero, i.e., delta-like, energy density. The aim of this work is to analyze this situation from a mathematical point of view, using the framework of Colombeau's theory of nonlinear generalized functions. It is shown that the physically unsatisfactory situation is mathematically perfectly defined and that one cannot aviod such situations when dealing with distributional valued field tensors.
We consider two types of Born-Infeld like nonlinear electromagnetic fields and obtain their interesting black hole solutions. The asymptotic behavior of these solutions is the same as that of Reissner-Nordstrom black hole. We investigate the geometric properties of the solutions and find that depending on the value of the nonlinearity parameter, the singularity covered with various horizons.
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…
We show that an incoming null-geodesic belonging to a plane passing through the origin and starting outside the outer horizon crosses the outer and the inner horizons. Then it turns at some point inside the inner horizon and approaches the inner horizon when the time tends to the infinity. We also construct a geometric optics solution of the Reissner-Nordstrom equation that has support in a neighborhood of the null-geodesic.
This master thesis discusses the Reissner-Nordström metric and the dirac equation in curved spaces in the pseudo-complex General Relativity (pc-GR) and reviews the original ansatz of pc-GR. It is written in German.
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.
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
We investigate retrolensing of sunlights reflected by a photon sphere and by a potential barrier near an antiphoton sphere around a Reissner-Nordström naked singularity. We apply the deflection angles of light rays in strong deflection limits to the retrolensing. We show that the retrolensing by the photon sphere around the Reissner-Nordström naked singularity can be brighter than the one around a Reissner-Nordström black hole because of the existence of the rays which reflected by the potential barrier.
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.
We show asymptotic completeness for the massive charged Dirac equation between the black hole and Cauchy horizons of a sub-extremal ((Anti-) De Sitter) Reissner-Nordström black hole.
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 calculate the expectation value of the stress energy tensor for a massless dilaton-coupled 2D scalar field propagating on an extremal Reissner-Nordstrom black hole formed by the collapse of a timelike shell, showing its regularity on the horizon.
We study the dynamics of a massive charged scalar wave which except its canonical coupling to gravity it is also coupled kinematically to Einstein tensor. We find that as the strength of the new coupling is increased the scattered wave off the horizon of a Reissner-Nordström black hole is superradiantly amplified resulting to the instability of the Reissner-Nordström spacetime.
It is shown that if two Reissner-Nordström space-times, both with the same mass m and charge e, glued together in the singularities, then the light ray in black hole of the first space-time can go continuously through the singularity into black hole of the second. The behavior of tidal forces near the Reissner-Nordström space-time singularity is examined by considering what happens between two particles falling freely towards the singularity.
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.
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.
In a previous work [E.M. Prodanov, R.I. Ivanov, and V.G. Gueorguiev, Reissner-Nordstrom Expansion, Astroparticle Physics 27 (150-154) 2007], we proposed a classical model for the expansion of the Universe during the radiation-dominated epoch based on the gravitational repulsion of the Reissner-Nordstrom geometry - naked singularity description of particles that "grow" with the drop of the temperature. In this work we model the Universe during the Reissner-Nordstrom expansion as a van der Waals gas and determine the equation of state.
Contrary to previous claims, it is shown that the expectation values of the quantum stress tensor for a massless scalar field propagating on a two-dimensional extreme Reissner-Nordstrom black hole are indeed regular on the horizon.
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…
In the framework of black hole spectroscopy, we extend the results obtained for a charged black hole in an asymptotically flat spacetime to the scenario with non vanishing negative cosmological constant. In particular, exploiting Hamiltonian techniques, we construct the area spectrum for an AdS Reissner-Nordstrom black hole.
The p-hierarchy of Schwarzschild type metrics obtained in a preceing paper is generalised here to a corresponding Reissner-Nordstrom (RN) type hierarchy in the presence of a point charge q in d-dimensions. Certain special features arising, concerning the horizons and the interior region, are discussed.
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.
The phase transition of Reissner-Nordstrom AdS_4 interacting with a massive charged scalar field has been further revisited. We found exactly one stable and one unstable quasinormal mode regions for the scalar field. The two of them are separated by the first marginally stable solution.
We calculate the expectation values of the stress-energy tensor for both a massless minimally-coupled and dilaton-coupled 2D field propagating on an extremal Reissner-Nordstrom black hole, showing its regularity on the horizon in contrast with previous claims in the literature.
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.
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.
A two-dimensional (2D) dilaton gravity model, whose static solutions have the same features of the Reissner-Nordstrom solutions, is obtained from the dimensional reduction of a four-dimensional (4D) string effective action invariant under S-duality transformations. The black hole solutions of the 2D model and their relationship with those of the 4D theory are discussed.
Massive charged and uncharged particles tunneling from commutative Reissner-Nordstrom black hole horizon has been studied with details in literature. Here, by adopting the coherent state picture of spacetime noncommutativity, we study tunneling of massive and charged particles from a noncommutative inspired Reissner-Nordstrom black hole horizon. We show that Hawking radiation in this case is not purely thermal and there are correlations between emitted modes. These correlations may provide a solution to the information loss problem. We also study thermodynamics of noncommutative horizon in thi…
Using standard coordinates, the Maxwell equations in the Reissner-Nordström geometry are written in terms of a couple of scalar fields satisfying Klein-Gordon like equations. The density of states is derived in the semi-classical approximation and the first quantum corrections to the black hole entropy is computed by using the brick-wall model.
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…
A previous evaluation of one-photon loop corrections to the energy-momentum tensor has been extended to particles with unit spin and speculations are presented concerning general properties of such forms.
We study gravitational lensing by a Reissner-Nordstrom (RN) black hole in the weak field limit. We obtain the basic equations for the deflection angle and time delay and find analytical expressions for the positions and amplifications of the primary and secondary images. Due to a net positive charge, the separation between images increases, but no change in the total magnification occurs.
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.
The geometry very near the horizon of a near-extreme Reissner-Nordstrom black hole is described by the direct product of a near-$AdS_2$ spacetime with a two-sphere. While near-$AdS_2$ is locally diffeomorphic to $AdS_2$ the two connect differently with the asymptotically flat part of the geometry of (near-)extreme Reissner-Nordstrom. In previous work, we solved analytically the coupled gravitational and electromagnetic perturbation equations of $AdS_2\times S^2$ and the associated connection problem with extreme Reissner-Nordstrom. In this paper, we give the solution for perturbations of near-…
The bound-state problem for an uncharged massive scalar particle in the field of a naked Reissner-Nordström singularity is approached by means of the quasiclassical Bohr-Sommerfeld quantization. An approximate analytical expression for the energy levels of the system is derived. It is shown that in order to obtain non-vanishing binding energies the masses of both the central object and the particle should be comparable with the Planck mass.
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…
We construct new charged solutions of the Einstein-Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher dimensional Reissner-Nordström spacetimes. For a negative cosmological constant these solutions are the charged generalizations of the topological nut-charged black hole solutions in higher dimensions. Finally, we discuss the global structure of such solutions and possible applications.
We investigate the superradiant instability of dyonic Reissner-Nordström (dRN) black holes with two charges under a charged massive scalar perturbation. Two conditions for possessing a trapping well are obtained from analyzing asymptotic scalar potential and far-region wave functions. It is clear that the superradiant instability is not allowed in the dRN black holes because the conditions for a trapping well are not compatible with the superradiance condition.
The formation of near-extremal Reissner-Nordstrom black holes in the S-wave approximation can be described, near the event horizon, by an effective solvable model. The corresponding one-loop quantum theory remains solvable and allows to follow analytically the evaporation process which is shown to require an infinite amount of time.
