We have shown analytically that radiation from a collapsing shell which leads to a charged black hole, whose exterior is described by the RN (Reissner-Nordström) metric (and hence the background spacetime is non-globally hyperbolic), is processed with a unitary evolution. For the analysis, we have used the Wheeler-deWitt formalism which in turn gave rise to a Schrödinger-like wave equation. We showed the existence of unitarity by proving that the trace of the squared density matrix of the outgoing radiation, from a quantized massless scalar field, is unity and that the conservation of probability holds for the wave function of the system.
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.
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 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.
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 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 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.
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 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 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.
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 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.
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.
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.
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.
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…
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.
A $2p + 5$ parametric family of black holes is constructed in dilaton--axion gravity with $p$ vector fields using a holomorphic representation of U--duality in three dimensions. The metric of the non--extremal black holes has a Reissner--Nordström type structure and generically possesses an internal horizon. However in the extremal limit the generic solution exhibits a dilatonic type null singularity. Only in the case of the orthogonal electric and magnetic charges (if $p>1$) the extremal solution may have a non--singular event horizon.
We examine the stability of extremal braneworld Reissner-Nordström black holes under massive charged scalar perturbations. We show that similar to the four-dimensional case, the superradiant amplification can occur in braneworld charged holes. More interestingly we find that when the spacetime dimension is higher than four, a trapping potential well can emerge outside the braneworld black hole. This potential well is the extra dimensional effect and does not exist in four dimensions. It triggers the superradiant instability of the extremal braneworld charged holes.
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.
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 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.
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 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.
We consider electrogeodesics on which the energy $E<0$ in the Reissner-Nordström metric. It is shown that outside the horizon there is exactly one turning point inside the ergoregion for such particles. This entails that such a particle passes through an infinite chain of black-white hole regions or terminates in the singularity. These properties are relevant for two scenarios of high energy collisions in which the presence of white holes is essential.
Recent numerical investigations have uncovered a surprising result: Reissner-Nordstrom-de Sitter black holes are unstable for spacetime dimensions larger than 6. Here we prove the existence of such instability analytically, and we compute the timescale in the near-extremal limit. We find very good agreement with the previous numerical results. Our results may me helpful in shedding some light on the nature of the instability.
We consider embedding diagrams for the Reissner-Nordström spacetime. We embed the $(r-t)$ and $(r-ϕ)$ planes into 3-Minkowski/Euclidean space and discuss the relation between the diagrams and the corresponding curvature scalar of the 2-metrics
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.
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.
The fundamental quasinormal resonances of charged Reissner-Nordström black holes due to charged scalar perturbations are derived {\it analytically}. In the WKB regime, $qQ\gg\hbar$, we obtain a simple expression for the fundamental quasinormal resonances: $ω=qQ/r_+-i2πT_{\text{BH}}(n+{1 \over 2})$, where $T_{\text{BH}}$ and $Q$ are the temperature and electric charge of the black hole and $q$ is the electric charge of the field. Remarkably, our results show that the relaxation dynamics of a perturbed Reissner-Nordström black hole may saturate the recently proposed universal relaxation bound.
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.
We obtain an analytic solution for accretion of a gaseous medium with a adiabatic equation of state ($P=ρ$) onto a Reissner-Nordström black hole which moves at a constant velocity through the medium. We obtain the specific expression for each component of the velocity and present the mass accretion rate which depends on the mass and the electric charge. The result we obtained may be helpful to understand the physical mechanism of accretion onto a moving black hole.
It is known that the extremal Reissner-Nordström black hole possesses a discrete conformal isometry that exchanges the black hole horizon with infinity. It is also known that the Reissner-Nordström-de Sitter spacetime posseses a similar discrete conformal isometry which exchanges the event horizon of the black hole with the cosmological horizon. In this short paper we will continue this line of thought and extend the conformal isometry of the latter spacetime and give an unphysical interpretation of the negative root.
The aim of this work is to apply WIMT to Gullstránd-Painlevé and Reissner-Nordström metrics in the framework of Weitzeböck Induced Matter Theory (WIMT). This is a newly developed method that extends Induced Matter Theory from a curved 5D manifold using the Weitzeböck's geometry, using the fact that the Riemann-Weitzeböck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles.
A concentric charged thin-shell encircling a Reissner-Nordström black hole screens the clectric / magnetic charge completely to match with an external Schwarzschild black hole. The negative mass thin-shell is shown to be stable against radial perturbations. It is shown further that by reversing the roles of inside Reissner-Nordström and outside Schwarzschild geometries the mass of the appropriate shell becomes positive.
The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner-Nordström black-hole spacetime are studied {\it analytically}. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein-Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum…
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.
Different geometrical and topological properties have been shown for two kinds of extreme Reissner-Nordstr$\ddot{o}$m-anti-de Sitter black holes. The relationship between the geometrical properties and the intrinsic thermodynamical properties has been made explicit.
It is shown that the extremal Reissner-Nordström black hole, the non-extremal one with multiple scattering particles, and the Schwarzschild black hole with radial head-on particles are stable under the collision of the particles near the horizon, if the back-reaction effect and the effect generated by gravity of particles are involved. Moreover, the collision near Reissner-Nordström black holes with astrophysically typical mass can not generate the Planck-scale center-of-mass energy. However, the head-on collision near the typical primordial black hole could just occur at the Planck-energy sca…
The Reissner--Nordström family of solutions can be understood to arise from the spherically symmetric sector of a nonlinear SO(2,1)/SO(1,1) sigma model coupled to three dimensional Euclidean gravity. In this context a group theoretical quantization is performed. We identify the observables of the theory and calculate their spectra.
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.
We show that the cold horizon of the extremal Reissner-Nordström can be considered as the throat of a thin-shell wormhole with zero total exotic matter and positive angular pressure. Such a wormhole is physical and stable against radial perturbations provided an appropriate perfect fluid exists at the throat.
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.
It is well known that the U(1) Reissner-Nordström black hole is stable within the framework of the Einstein-Maxwell theory. However, the SU(2) Reissner-Nordström black-hole solution of the coupled Einstein-Yang-Mills equations is known to be unstable. In fact, this magnetically charged black hole is characterized by an infinite set of unstable (growing in time) perturbation modes. In the present paper we study {\it analytically} the instability resonance spectrum of weakly-magnetized SU(2) Reissner-Nordström black holes. In particular, we obtain explicit analytical expressions for the infinite…
Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordström black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordström black hole spacetime. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.
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…
A class of curves with special conformal properties (conformal curves) is studied on the Reissner-Nordström spacetime. It is shown that initial data for the conformal curves can be prescribed so that the resulting congruence of curves extends smoothly to future and past null infinity. The formation of conjugate points on these congruences is examined. The results of this analysis are expected to be of relevance for the discussion of the Reissner-Nordström spacetime as a solution to the conformal field equations and for the global numerical evaluation of static black hole spacetimes.
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.
