Reissner-Nordstrom Research Articles

Quasinormal modes of the electric potential in the 4 dimensional anti de Sitter Reissner-Norstöm black hole spacetime with scalar hair

In this study, analytical calculations are performed to assess the quasinormal modes (qnm) of the perturbed electromagnetic potential within the a four-dimensional spacetime of the Reissner-Nordström (RN) anti-de Sitter (AdS) black holes which are dressed with scalar hair. The black holes serve as the solutions for the Einstein-Maxwell theory under a negative cosmological constant and conformally-coupled real self-interacting scalar field. When the strength of the scalar field is suitable, phase transition of the black holes occurs to create a new form of MTZ black holes. The electromagnetic field can then be perturbed and the qnm and their frequencies calculated in order to meet the boundary conditions both at the horizon and at the far distant region from the new MTZ black hole. In order to address a simplified version of this problem, this study investigates the case whereby the mass of the MTZ black hole is significantly less than the AdS radius.

Super-Penrose process for extremal charged white holes

We consider collision of two particles 1 and 2 near the horizon of the extremal Reissner–Nordström (RN) black hole that produces two other particles 3 and 4. There exists such a scenario that both new particles fall into a black hole. One of them emerges from the white hole horizon in the asymptotically flat region, and the other one oscillates between turning points. However, the unbounded energies [Formula: see text] at infinity (super-Penrose process (SPP)) turn out to be impossible for any finite angular momenta [Formula: see text]. In this sense, the situation for such a white hole scenarios is opposite to the black hole ones, where the SPP is found earlier to be possible for the RN metric even for all [Formula: see text]. However, if [Formula: see text] themselves are unbounded, the SPP does exist for white holes.

Lorentz violation, quantum tunneling, and information conservation * *Supported by the National Natural Science Foundation of China (11903025), and by the starting fund of China West Normal University (18Q062), and by the Natural Science Foundation of Sichuan Education Department (17ZA0294), and by the Research Project of Si Chuan MinZu College (XYZB18003ZA)

In this paper, by introducing the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) suppressed by the second power , we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordström (RN) black hole. It was determined that the LIV speeds up black hole evaporation. As a result, the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle. However, at the same energy level, it was insensitive to changes in the charge of the radiation particle. This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity. Moreover, when the effect of the LIV was included, we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation. We also determined that black hole radiation via tunneling is an entropy conservation process, and no information loss occurred during radiation, where the interpretation of the entropy of a black hole is addressed. Finally, we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.

Hairy black holes by gravitational decoupling

Black holes with hair represented by generic fields surrounding the central source of the vacuum Schwarzschild metric are examined under the minimal set of requirements consisting of i) the existence of a well defined event horizon and ii) the strong or dominant energy condition for the hair outside the horizon. We develop our analysis by means of the gravitational decoupling approach. We find that trivial deformations of the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanism to evade the no-hair theorem based on a primary hair associated with the charge generating these transformations. Under the above conditions i) and ii), this charge consistently increases the entropy from the minimum value given by the Schwarzschild geometry. As a direct application, we find a non-trivial extension of the Reissner-Nordstrom black hole showing a surprisingly simple horizon. Finally, the non-linear electrodynamics generating this new solution is fully specified.

Dynamical transition from a naked singularity to a black hole

We show that a Reissner–Nordström (RN) black hole can be formed by dropping a charged thin dust shell onto a RN naked singularity. This is in contrast to the fact that a RN naked singularity is prohibited from forming by dropping a charged thin dust shell onto a RN black hole. This implies the strong tendency of the RN singularity to be covered by a horizon in favor of cosmic censorship. We show that an extreme RN black hole can also be formed from a RN naked singularity by the same process in a finite advanced time. We also discuss the evolution of the charged thin dust shells and the causal structure of the resultant space–times. a a The statements expressed in this paper are those of the authors and do not represent the views of Sumitomo Mitsui Banking Corporation or its staff.

On the quantization of the extremal Reissner-Nordström black hole

Following Rosen's quantization rules, two of the authors (C. Corda and F. Feleppa) recently described the Schwarzschild black hole (BH) formed after the gravitational collapse of a pressureless “star of dust” in terms of a “gravitational hydrogen atom”. Here we generalize this approach to the gravitational collapse of a charged object, namely, to the geometry of a Reissner-Nordström BH (RNBH) and calculate the gravitational potential, the Schrödinger equation and the exact solutions of the energy levels of the gravitational collapse. By using the concept of BH effective state, previously introduced by one of us (CC), we describe the quantum gravitational potential, the mass spectrum and the energy spectrum for the extremal RNBH. The area spectrum derived from the mass spectrum finds agreement with a previous result by Bekenstein. The stability of these solutions, described with the Majorana approach to the Archaic Universe scenario, shows the existence of oscillatory regimes or exponential damping for the evolution of a small perturbation from a stable state.

Extended phase space thermodynamics for black holes in a cavity

In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius rB to include V=4pi {r}_B^3/3 as a thermodynamic volume. The thermodynamic behavior of Schwarzschild and Reissner-Nordstrom (RN) black holes is then investigated in the extended phase space. In a canonical ensemble at constant pressure, we find that the aforementioned thermodynamic behavior is remarkably similar to that of the anti-de Sitter (AdS) counterparts with the cosmological constant being interpreted as a pressure. Specifically, a first-order Hawking-Page-like phase transition occurs for a Schwarzschild black hole in a cavity. The phase structure of a RN black hole in a cavity shows a strong resemblance to that of the van der Waals fluid. We also display that the Smarr relation has the same expression in both AdS and cavity cases. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.

Quantum thermodynamics in the interior of a Reissner–Nordström black-hole

We study the interior of a Reissner-Nordstr\"om Black-Hole (RNBH) using Relativistic Quantum Geometry, which was introduced in some previous works. We found discrete energy levels for a scalar field from a polynomial condition for the Heun Confluent functions expanded around the effective causal radius $r_*$. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: $E_n\, r_{*,n}=\hbar/2$, and the charged mass is discretized and distributed in a finite number of states. The classical RNBH entropy is recovered as the limit case where the number of states is very large, and the RNBH quantum temperature depends on the number of states in the interior of the RNBH. This temperature, depending of the number of states of the RNBH, is related with the Bekeinstein-Hawking (BH) temperature: $T_{BH} \leq T_{N} < 2\,T_{BH}$.

Classical tools for antipodal identification in Reissner–Nordström spacetime

We extend the discussion of the antipodal identification of black holes to the Reissner–Nordström (RN) spacetime by developing the classical tools necessary to define the corresponding quantum field theory (QFT). We solve the massless Klein–Gordon equation in the RN background in terms of scattering coefficients and provide a procedure for constructing a solution for an arbitrary analytic extension of RN. The behavior of the maximally extended solution is highly dependent upon the coefficients of scattering between the inner and outer horizons, so we present the low-frequency behavior of, and numerical solutions for, these quantities. We find that, for low enough frequency, field amplitudes of solutions with purely positive or negative frequency at each horizon will acquire only a phase after passing both the inner and outer horizons, while at higher frequencies the amplitudes will tend to grow exponentially either to the future or to the past, and decay exponentially in the other direction. Regardless, we can always construct a basis of globally antipodal symmetric and antisymmetric solutions for any finite analytic extension of RN. We have characterized this basis in terms of positive and negative frequency solutions for future use in constructing the corresponding QFT.

Canonical Quantization of the Expansion Scalar for the Reissner-Nordstrom Metric

The outer event horizon r+ of a Reissner-Nordstrom black hole is shown to satisfy the conditions of a Non-Expanding Horizon and the inner horizon r− is assumed to be dynamically evolving in area as no restrictions are imposed. An area evolution law is formulated, using the expansion scalar, keeping in mind the imposed conditions. It is later shown that the expansion scalar is the black hole analogue to the thermodynamic heat flow, just as area of a horizon is the black hole analogue of entropy. It is shown that the expansion scalar and the thermodynamic heat of the horizon form a canonical pair and the Lagrangian and Hamiltonian equations are formulated for this condition. From the equations, the expansion is quantized and the Heisenberg Inequaltity for this system is formulated.

“Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole

A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the re-parametrization covariance r→f(r˜). As a result, the evolution of states with respect to the parameter r and the probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for Dirac’s delta and Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside this, a criterion is presented to adjudicate which, between two singular spacetimes, is “more” or “less” singular. Two ways to adjudicate the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with those of a 3D electromagnetic pp-wave spacetime is revealed.

Quasinormal modes of charged fields in Reissner-Nordström backgrounds by Borel-Padé summation of Bender-Wu series

We extend recent work of Hatsuda on the computation of quasinormal mode frequencies via analytic continuation of bound state energies and Borel-Pade resummation of the Bender-Wu perturbation series to the case of charged fields in the background of Reissner-Nordstrom black holes. We compare the quasinormal mode frequencies obtained in this manner to calculations using Leaver's method of continued fractions, and find good agreement for damped modes (DMs) with imaginary part remaining finite in the extremal limit. We also present numerical evidence that the frequencies of certain zero-damped modes (ZDMs) with imaginary part tending to zero in the extremal limit can be computed when constructing the Bender-Wu expansion about a peak of the potential inside the outer horizon of the black hole.

Gauss Symbol and Unified Theory of Gravity and Electromagnetic Field in Reissner-Nordstrom and Kerr-Newman Solution

Solutions of unified theory equations of gravity and electromagnetism satisfy Einstein Maxwe ll equation. Hence, solutions of the unified theory is Reissner Nordstrom solution , Kerr Newman solution in vacuum. In this careful point, Einstein gravity field equation’s energy momentum tensor has two sign. Therefore, according to the solution, the sign is treated. We found in revised Einstein gravity tensor equation , the condition is satisf ied by 2 order contravariant metric tensor two times product and Gauss symbol.

Test particle orbits around regular black holes in general relativity combined with nonlinear electrodynamics

We provide detailed analysis of the curvature structure of the spacetime around regular black holes (RBHs) governed by general relativity (GR) combined with nonlinear electrodynamics (NED), characterized by electric charge $Q$, and degree of nonlinearity $n$. We consider special class of the backgrounds introduced by Toshmatov et al. [Phys. Rev. D 98, 028501 (2018)] that have proper Maxwell weak-field limit of the NED sector. We also study the motion of uncharged and charged particles in the RBH background. We determine shadows of such black holes (BHs) using the effective geometry governing motion of photons in the background of NED RBHs. The analysis of circular motion enables to determine innermost stable circular orbits (ISCO) and marginally bound orbits (MBO). We show that the radius of ISCO and MBO for neutral particles decreases as the parameters of the RBH $Q$ and $n$ increase for the fixed value of the BH mass. We demonstrate that for the electrically charged particles properties of the circular orbits strongly depend on their Coulomb interaction with the RBH charge. The dependence of the ISCO radius on the particle specific charge $q$ and the RBH parameters is rather complex, but for the attractive Coulomb interaction there is a general feature (independent of $n$) giving a limiting value of the intensity of this interaction $q{Q}_{\mathrm{max}}$ behind which no stable circular orbits are allowed around the RBH. Comparison of the RBH with Reissner-Nordstr\"om black holes (RNBH) shows that for the same electric charges of these backgrounds the location of the relevant orbits is at substantially smaller radii for the RBH, demonstrating thus a strong influence of the NED effects. The analysis of ISCO radius of test particles has shown that the charge of RBH $Q$ can mimic the rotation parameter of Kerr BH up to the value $a=0.8M$. We have also shown that the RN BH charge can mimic the rotation parameter up to $a=0.5M$ and the RBH charge up to $Q=0.2M$. Applications from observational data to the parameters of the supermassive black holes (SMBHs) at the galactic center Messier 87 (M87) and Milky Way so called Sagittarius ${\mathrm{A}}^{*}$ (${\mathrm{Sgr}\text{ }A}^{*}$) give the mimic value for the RBH charge parameter for the rotation parameter of M87 to be ${10}^{3}Q\ensuremath{\approx}277.5{6}_{\ensuremath{-}1.26}^{+3.82}$, while for ${\mathrm{Sgr}\text{ }A}^{*}$ there is ${10}^{3}Q\ensuremath{\approx}187.3{3}_{\ensuremath{-}26.4}^{+27.6}$. Moreover, it is shown that the RN BH charge cannot mimic the rotation parameter of the SMBH M87, however, it can mimic the spin parameter of ${\mathrm{Sgr}\text{ }A}^{*}$ at ${10}^{3}{Q}_{\mathrm{RN}}/M=828.7{1}_{\ensuremath{-}60.94}^{+70.58}$.

The Symmetry of the Interior and Exterior of Schwarzschild and Reissner–Nordstrom Black Holes—Sphere vs. Cylinder

One can question the relationship between the symmetries of the exterior and interior of black holes with an isotropic and static exterior. This question is justified by the variety of recent findings indicating substantial or even dramatic differences in the properties of the exterior and interior of isotropic, static black holes. By invoking some of these findings related to a variety of the thought experiments with freely falling or uniformly accelerated test particles, one can establish the dynamic properties of the interior, which turn out to be equivalent to anisotropic cosmology, simultaneously expanding and contracting, albeit in different directions. In order to illustrate the comparison between the symmetry of the exterior vs. the interior, we apply conventional t, r, θ, φ coordinates to both of these ranges, although on the horizon(s) they display singular behavior. Using a simple approach based on co-moving and freely falling observers, the dynamics of the cylindrically shaped interior are explored. That enables us to present schematic snapshots of the interior of a Schwarzschild black hole, expanding along its cylindrical axis and contracting along its spherical base, as well as the interior of a Reissner–Nordström black hole, expanding first and then contracting along the cylindrical axis up to the terminal instant r =r−.

Einstein-Maxwell-scalar black holes: The hot, the cold and the bald

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function f(ϕ), between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordström (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: f(Φ)=1+αΦ4. The domain of existence of the scalarised BHs, for fixed α, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the S-deformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [Myers-Perry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.

Thermal phase transition in F(R) -charged AdS4 scalar theory

We investigate instabilities of $F(R)$-charged ${\mathrm{AdS}}_{4}$ black holes by a massive charged scalar field in a linear perturbation regime. We study tachyonic instabilities as the near horizon scalar condensation in a model of $F(R)$ gravity with planar horizon and investigate properties of possible phase transitions. The results show that such transitions are sensitive to the first derivative of $F(R)$ with respect to $R$ in that the larger its value, the higher the critical temperature, thus resulting in a new generation of high-temperature superconductors. Also, for a certain range of parameters, $F(R)$-charged ${\mathrm{AdS}}_{4}$ black holes suffer from superradiant instability. We consider the effects of the scalar mass and charge on such instabilities and conclude that Reissner-Nordstrom (RN) black holes decay into small hairy black holes that have a charged scalar condensate floating near the horizon. It is shown that the existence of phase transition at the critical temperature leading to a hairy black hole solution emerges for $T&lt;{T}_{c}$, while RN black holes exist for $T&gt;{T}_{c}$. The effect of $F(R)$ on the critical temperature is subsequently investigated in the case of superradiant instability, showing that higher critical temperatures would be possible in $F(R)$ gravity. We also check the stability of hairy black holes and show that the resulting hairy solution can be considered as a possible endpoint of superradiant instability of a small charged black hole.

Scattering and absorption sections of nonlinear electromagnetic black holes

The expression of the impact parameter, in the analysis for classical and semiclassical scattering cross sections for black holes, is obtained with nonlinear electrodynamics (NLED) while the absorption section is studied with the sinc approximation in the eikonal limit considering NLED. As an illustration, we calculate the classical and semiclassical scattering as well as the absorption sections for three black holes under NLED, the regular magnetic Bardeen and Bronnikov black holes and the singular Euler-Heisenberg black hole. All are compared with the sections of their linear electromagnetic counterpart, the Reissner-Nordstrom (RN) black hole. The comparison shows how NLED affects the sections as well as the variation with respect to the Reissner-Nordstrom sections, in some cases these variations are small.

Role of Gravitation in Elementary Particle Structure

It is shown in the tetrad representation that there are Reissner–Nordstrom solutions describing systems with a finite action and total inertial mass equal to the gravitational mass. These systems consist of entirely electromagnetic and gravitational fields. There are not any massive point-charges inside them. The system is called ‘‘the classical electron’’ if its charge is equal to $${-}4.80\times 10^{-10}$$ esu. Its electromagnetic field is localized in a space region of about $$10^{-34}$$ cm. The total stress tensor for the classical electron is shown to be identically zero. This means that there is no need in an additional surface-tension of unknown nature preventing the system disintegration, as it takes place in the Lorentz electron model. The hypothesis that gravitation can play a crucial role in the structure of all elementary particles is discussed.

Thermodynamic studies with modifications of entropy: different black holes embedded in quintessence

Here we study the thermodynamic properties of black holes like Reissner–Nordstrom black hole and Bardeen AdS black hole embedded in quintessence. We analyze the thermodynamic volume and naive geometric volume of Bardeen AdS black hole surrounded by the quintessence and find that they are not equal, rather the thermodynamic volume has grater value than naive geometric volume. We also analyze all the thermodynamic properties by plotting different graphs and interpret them physically for both the black holes. We compute the “cosmic-Censorship-Inequality” for the same black holes. further, we investigate their thermal stabilities by calculating the thermal heat capacity and study in different regimes. Finally, we compute the logarithmic correction to the entropy assuming the quantum fluctuations around the thermal equilibrium and investigate the corresponding thermodynamics.