We show that the closed-form monotone solution linking two different vacuum states, for the exterior Yang--Mills wave equation over the extremal Reissner--Nordström spacetime found in a recent work of Bizoń and Kahl, is the unique solution to an associated domain-wall type energy minimization problem. We also derive the accompanying interior Yang--Mills wave equation within the same formalism. We obtain a few more closed-form solutions, regular and singular, among other solutions of oscillatory behavior, and discuss several interesting features of the solutions based on some energy consideration.
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.
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.
We show that generic linear perturbations $ψ$ solving $\Box_g ψ+ \fracα{l^2} ψ=0$ on Reissner-Nordström-AdS black holes have infinite local energy at the Cauchy horizon. Combined with the result of arXiv:1812.06142 that such perturbations $ψ$ remain uniformly bounded and extend continuously across the Cauchy horizon, this settles the linear analog of the Strong Cosmic Censorship conjecture for Reissner-Nordström-AdS: the $C^0$-formulation is false but the $H^1$-formulation is true.
The aim of present work is to extend the application of Weitzeböck Induced Matter Theory (WIMT) to a dyonic Reissner-Nordström Black Hole (RNBH), by proposing a condition compatible with a quantization relation between gravitational mass and both magnetic and electric charges from a geometric product defined as an invariant in 5D.
The scalarization of Reissner-Nordström black holes was recently proposed in the Einstein-Maxwell-scalar theory. Here, we show that the appearance of the scalarized Reissner-Nordström black hole is closely related to the Gregory-Laflamme instability of the Reissner-Nordström black hole without scalar hair.
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.
We study the stability of extreme Reissner-Nordström-AdS black hole under massless scalar perturbations. We show that the perturbation on the horizon of the extreme Reissner-Nordström-AdS black hole experiences a power-law decay, instead of an exponential decay as observed in the nonextreme AdS black hole. On the horizon of the extreme Reissner-Nordström-AdS black hole, the blow up happens at lower order derivative of the scalar field compared with that of the extreme Reissner-Nordström black hole, which shows that extreme AdS black holes tend to instability in comparison to black holes in asy…
We reinterpret recent work on extremal Reissner- Nordstrøm black holes to argue that the mass is a measure of the gravitational entropy. We also find that the entropy of scalar fields in this background has a stronger divergence than usual.
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.
This paper is devoted to the study of the Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacetimes. Here, we find the necessary and sufficient conditions on the parameters of the Reissner-Nordstrøm-de Sitter metric -namely, the mass, the charge, and the cosmological constant- to have three horizons. Under this conditions, we prove that there is only one photon sphere and …
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.
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.
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.
We analyze in detail the highly damped quasinormal modes of $D$-dimensional extremal Reissner-Nordstr$\ddot{\rm{o}}$m and Reissner-Nordstr$\ddot{\rm{o}}$m-de Sitter black holes. We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide. We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.
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.
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.
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.
We study all transverse deformations of the extremal Reissner-Nordström-(A)dS horizon in the Einstein-Maxwell theory. No symmetry assumptions are needed. It is shown that for the generic values of the charge, the only allowed deformation is spherically symmetric. However, it is shown that for fine-tuned values of a charge, the space of deformations is larger, yet still finite-dimensional.
We consider smooth solutions of the wave equation, on a fixed black hole region of a subextremal Reissner-Nordström (asymptotically flat, de Sitter or anti-de Sitter) spacetime, whose restrictions to the event horizon have compact support. We provide criteria, in terms of surface gravities, for the waves to remain in $C^l$, $l\geq 1$, up to and including the Cauchy horizon. We also provide sufficient conditions for the blow up of solutions in $C^1$ and $H^1$.
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.
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 work we address the study of null geodesics in the background of Reissner-Nordström Anti de Sitter black holes. We compute the exact trajectories in terms of elliptic functions of Weierstrass, obtaining a detailed description of the orbits in terms of charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.
We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner-Nordstrøm-de Sitter black bole spacetime. This is done using uniform energy decay results that we obtain in a separate paper, to show that the trace operators are injective and have closed ranges. We then solve the Goursat problem (characteristic Cauchy problem) for Maxwell fields on the null boundaries showing that the trace operators are also surjective.
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 solve the condundrum on whether the molecules of the Reissner-Nordström black hole interact through the Ruppeiner thermodynamic geometry, basing our study on the concept of the black hole molecule proposed in [Phys. Rev. Lett. 115 (2015) 111302] and choosing the appropriate extensive variables. Our results show that the Reissner-Nordström black hole is indeed an interaction system that may be dominated by repulsive interaction. More importantly, with the help of a novel quantity, namely the thermal-charge density, we describe the fine micro-thermal structures of the Reissner-Nordström black…
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.
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.
Recent work that treats the Hawking radiation as a semi-classical tunnelling process from the four-dimensional Schwarzschild and Reissner-Nordstrom black holes is extended to the case of higher dimensional Reissner-Nordstrom-de Sitter black holes. The result shows that the tunnelling rate is related to the change of Bekenstein-Hawking entropy and the exact radiant spectrum is no longer precisely thermal after considering the black hole background as dynamical and incorporating the self-gravitation effect of the emitted particles when the energy conservation and electric charge conservation are…
We present a quantum description of electrically charged spherically symmetric black holes given by coherent states of gravitons in which both the central singularity and the Cauchy horizon are not realised.
A conjecture by Hod states that for the black hole horizon the spacing of its area spectrum is determined by the asymptotic value of its quasinormal frequencies. Recently to overcome some difficulties, Maggiore proposes some changes to the original Hod's conjecture. Taking into account the modifications proposed by Maggiore we calculate the area spectrum of the d-dimensional Reissner-Nordstrom black hole in the small charge limit.
A family of deformed AdS4-Reissner-Nordström black branes, governed by a free parameter, is derived using the ADM formalism, in the context of the membrane paradigm. Their new event horizons, the Hawking temperature and other aspects are scrutinized. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio for the deformed AdS4-Reissner-Nordström metric. The Killing equation is shown to yield new values for the free parameter and the shear viscosity-to-entropy ratio is used to derive a reliable range for tidal charge.
It is shown that the scalar wave equation in the near-horizon limit respects a hidden SL(2,R) invariance in the Reissner-Nordstrom (RN) black hole spacetimes. We use the SL(2,R) symmetry to determine algebraically the purely imaginary quasinormal frequencies of the RN black hole. We confirm that these are exactly quasinormal modes of scalar perturbation around the near-extremal black hole.
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.
A simple model of spacetime foam, made by $N$ Reissner-Nordström wormholes with a magnetic and electric charge in a semiclassical approximation, is taken under examination. The Casimir-like energy of the quantum fluctuation of such a model is computed and compared with that one obtained with a foamy space modeled by $N$ Schwarzschild wormholes. The comparison leads to the conclusion that a foamy spacetime cannot be considered as a collection of $N$ Reissner-Nordström wormholes but that such a collection can be taken as an excited state of the foam.
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.
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 obtain a Schwarzschild and a Reissner-Nordstrom emergent black holes, by exploring the torsion dynamics in a generalized curvature formulation, underlying an effective D4-brane on S1. It is shown that a constant effective metric, sourced by a background fluctuation in B2-potential, on a D3-brane receives a dynamical quantum correction in presence of an electric charge.
We develop a nonlinear perturbation theory of Reissner-Nordström black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial sector. Gravitational part of these equations is similar to Regge-Wheeler and Zerilli equations with source and additional coupling to the electromagnetic sector. We construct solutions to the inhomogeneous part of wave equations in terms of sources for Einstein-Maxwell equations. We discuss $\ell=0$ and $ \ell=1$ cases separately.
We study the collision of two Reissner-Nordström gravitational shock waves in AdS and show that the charge completely prevents the formation of marginally trapped surfaces of the Penrose type with topology S^(D-2), independently of the energy and the value of the impact parameter. In the case of head-on collisions, a numerical analysis shows that no trapped surfaces with topology S^1 \times S^(D-3) form either.
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.
The study of the motion of photons around massive bodies is one of the most useful tools to know the geodesic structure associated with said gravitational source. In the present work, different possible paths projected in an invariant hyperplane are investigated, considering five-dimensional Reissner-Nordström anti-de Sitter black hole. Also, we study some observational test such as the bending of light and the Shapiro time delay effect. Mainly, we found that the motion of photons follows the hippopede of Proclus geodesic, which is a new type of trajectory of second kind, being the Limaçon of …
We describe a non-minimal higher-derivative extension of Einstein-Maxwell theory in which electrically-charged black holes and point charges have globally regular gravitational and electromagnetic fields. We provide an exact static spherically symmetric solution of this theory that reduces to the Reissner-Nordström one at weak coupling, but in which the singularity at $r=0$ is regularized for arbitrary mass and (non-vanishing) charge. We discuss the properties of these solutions and comment on the physical significance of our results.
We find a new instability in the four-dimensional Reissner-Nordstrom-de Sitter black holes against charged scalar perturbations with vanishing angular momentum, $l=0$. We show that such an instability is caused by superradiance. The instability does not occur for an larger angular index, as explicitely proven for $l=1$. Our results are obtained from a numerical investigation of the time domain profiles of the perturbations.
The stress-energy tensor of a free quantized scalar field is calculated in the extreme Reissner-Nordström black hole spacetime in the zero temperature vacuum state. The stress-energy appears to be regular on the event horizon, contrary to the suggestion provided by two-dimensional calculations. An analytic calculation on the event horizon for a thermal state shows that if the temperature is nonzero then the stress-energy diverges strongly there.
Hawking radiation originates from a "quantum atmosphere" around black holes, not necessarily from the vicinity of the horizon. We examine and discuss the properties of quantum atmospheres of asymptotically flat Reissner-Nordström black holes, which extends further and further away from the black hole as extremality is approached, though arguably it becomes indistinguishable from normal vacuum fluctuation at spatial infinity. In addition, following our previous findings on re-writing the Hawking temperature of a Kerr black hole in terms of a "spring constant", we generalize the same notion to t…
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.
For the radial motion of massive particles with large angular momenta in Schwarzschild geometry and that of massive charged particles with large angular momenta or energy in a particular range in Reissner--Nordström geometry, there exist classically forbidden regions on the outside of the respective event horizons which scatter certain infalling geodesics or screen some of the black holes' evaporation by reflecting the emitted particles back into the black holes. Quantum tunneling across this forbidden regions is studied.
In this work we derive a general expression for the greybody factor of non-minimally coupled scalar fields in Reissner-Nordström-de Sitter spacetime in low frequency approximation. In particular case of zero momentum, greybody factor tends to zero in low frequency limit as frequency squared goes to zero for non-vanishing coupling. We also elaborate the significance of the results by giving formulae of differential energy rate and general absorption cross section. The greybody factor gives insight into the spectrum of Hawking radiations.
We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our estimates hold up to and including the event horizon. The fundamental new aspect of this problem is the degeneracy of the redshift on the event horizon. Several new analytical features of degenerate horizons are also presented.
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.
