It has been conjectured that black hole interacting with its surroundings will obey the Generalized Second Law ($GSL$) of thermodynamics. Conservation of $GSL$ is due to the fully thermal nature of Hawking radiation and an upper bound on entropy. We study these aspects for a Reissner-Nordstr$\ddot{\textbf{o}}$m ($RN$)black hole and conjecture that $GSL$ may be conserved if the equation of state of radiation near the horizon is modified. An upper bound on $S/E$, similar to the Bekenstein form evolves in the calculation.
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.
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 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…
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 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 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.
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.
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.
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.
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.
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 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.
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.
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…
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…
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.
We study thermodynamic quantities and examine the stability of a black hole in a cavity inspired by the noncommutative geometry. It turns out that thermodynamic behavior of the noncommutative black hole is analogous to that of the Reissner-Nordström black hole in the near extremal limit. Moreover, we identify the noncommutative parameter with the squared electric charge with some constants.
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.
Allowing for scale dependence of the gravitational couplings leads to a generalization of the corresponding field equations. In this work, those equations are solved for the Einstein-Hilbert and the Einstein-Maxwell case, leading to generalizations of the (Anti)-de Sitter and the Reissner-Nordström black holes. Those solutions are discussed and compared to their classical counterparts.
Starting from Israel equations for the spherically symmetric thin shells we introduce the effective potential and show how it can be used in constructing, without further thorough investigation, the corresponding Carter-Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. We demonstrate, how this new method works, by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner-Nordström electro-vacuum manifolds.
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 discuss the phase transition between non-extremal and extremal Reissner-Nordström black holes. This transition is considered as the $T \to 0$ limit of the transition between the non-extremal and near-extremal black holes. We show that an evaporating process from non-extremal black hole to extremal one is possible to occur, but its reverse process is not possible to occur because of the presence of the maximum temperature. Furthermore, it is shown that the Hawking-Page phase transition between small and large black holes unlikely occurs in the AdS Reissner-Nordström black holes.
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.
In the eikonal regime, we analytically calculate quasinormal resonance frequencies for massless scalar perturbations of the higher-dimensional Reissner--Nordström (RN) black holes. Remarkably, we find that the higher-dimensional RN black holes coupled with the massless scalar fields have the fastest relaxation rates in the Schwarzschild limit, this is qualitatively different from the four-dimensional case where the black hole with non-vanishing charge has the fastest relaxation rate.
We study isoperimetric surfaces in the Reissner-Nordström spacetime, with emphasis on the cuasilocal inequality between area and charge. We analyze the stability of the isoperimetric spheres and we found that there is a lower bound on the area in terms of the charge, and that the inequality is saturated in the transition from the superextremal to the subextremal case. We also derive a general inequality between area and charge for stable isoperimetric surfaces in maximal electro-vacuum initial data.
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 investigate the general relativistic magnetohydrodynamic (GRMHD) equations for cold plasma around the Reissner-Nordström black hole. Applying 3+1 spacetime split we linearize the perturbed equations for non-magnetized/magnetized plasma in both rotating and non-rotating background. By Fourier analyze we then derive dispersion relations and investigate the existence of waves with positive angular frequency in the vicinity of the black hole horizon. The analysis finds propagation of negative phase and group velocities for rotating magnetized surroundings.
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 singularity of the solutions obtained before in the teleparallel theory of gravitation is studied. Also the stability of these solutions is studied using the equations of geodesic deviation. The condition of stability is obtained. From this condition the stability of Schwarzschild solution can be obtained.
In order to specify a foliation of spacetime by spacelike hypersurfaces we need to place some restriction on the initial data and from this derive a way to calculate the lapse function $α$ which measures the proper time and interval between neighbouring hypersurfaces along the normal direction. Here we study a prescribed slicing known as the Constant Mean Curvature (CMC) slicing. This slicing will be applied to the Reissner-Nordström metric and the resultant slices will be investigated and then compared to those of the extended Schwarzschild solution.
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.
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.
We present the generalized Reissner-Nordström solution of the field equations of metric-affine gravity (MAG), endowed with electric and magnetic charges, as well as with gravito-electric and gravito-magnetic charges and a cosmological constant term. Moreover, the case $M=e_o$, i.e. mass equal to electric charge and $λ=0$, corresponds to an electrically and magnetically charged monopole. Also further multipole solutions are obtained. The charge assignments of the solutions is discussed.
