The anomalous decay rate of the quasinormal modes occurs when the longest-lived modes are the ones with higher angular number. Such behaviour has been recently studied in different static spacetimes, for scalar and fermionic perturbations, being observed in both cases. In this work, we extend the existent studies to the charged spacetimes, namely, the Reissner-Nordström, the Reissner-Nordström-de Sitter and the Reissner-Nordström-Anti-de Sitter black holes. We show that the anomalous decay rate behaviour of the scalar field perturbations is present for every charged geometry in the photon sphere modes, with the existence of a critical scalar field mass whenever $Λ\geq 0$. In general, this critical value of mass increases with the raise of the black hole charge, thus rendering a minimum in the Schwarzschild limit. We also study the dominant mode/family for the massless and massive scalar field in these geometries showing a non-trivial dominance of the spectra that depends on the black hole mass and charge.
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 calculate the expectation value of the stress energy tensor for a massless dilaton-coupled 2D scalar field propagating on an extremal Reissner-Nordstrom black hole formed by the collapse of a timelike shell, showing its regularity on the horizon.
We study the dynamics of a massive charged scalar wave which except its canonical coupling to gravity it is also coupled kinematically to Einstein tensor. We find that as the strength of the new coupling is increased the scattered wave off the horizon of a Reissner-Nordström black hole is superradiantly amplified resulting to the instability of the Reissner-Nordström spacetime.
It is shown that 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.
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.
In the framework of black hole spectroscopy, we extend the results obtained for a charged black hole in an asymptotically flat spacetime to the scenario with non vanishing negative cosmological constant. In particular, exploiting Hamiltonian techniques, we construct the area spectrum for an AdS Reissner-Nordstrom black hole.
The 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.
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.
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.
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.
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.
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 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.
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…
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.
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.
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 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.
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.
The quasinormal modes of the Reissner-Nordström de Sitter black hole for the massless Dirac fields are studied using the Pöshl-Teller potential approximation. We find that the magnitude of the imaginary part of the quasinormal frequencies decreases as the cosmological constant or the orbital angular momentum increases, but it increases as the charge or the overtone number increases. An interesting feature is that the imaginary part is almost linearly related to the real part as the cosmological constant changes for fixed charge, and the linearity becomes better as the orbital angular momentum …
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.
The relation between the quasinormal modes (QNMs) and the second order thermodynamic phase transition (SOTPT) for the Reissner-Nordström (RN) black hole is studied. It is shown that the quasinormal frequencies of the RN black hole start to get a spiral-like shape in the complex $ω$ plane and both the real and imaginary parts become the oscillatory functions of the charge if the real part of the quasinormal frequencies arrives at its maximum at the second order phase transition point of Davies for given overtone number and angular quantum number. That is to say, we can find out the SOTPT point …
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.
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
The entropy of charged black hole is calculated by using the partition function evaluated at radial geodesics confined under horizons. We establish two quantum phase states inside the black hole and a transition between them.
