Extremal Reissner Research Articles

Instability of Gravitational and Electromagnetic Perturbations of Extremal Reissner–Nordström Spacetime

We study the linear stability problem to gravitational and electromagnetic perturbations of the extremal, |Q|=M,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ |Q|=M, $$\\end{document} Reissner–Nordström spacetime, as a solution to the Einstein–Maxwell equations. Our work uses and extends the framework [28, 32] of Giorgi, and contrary to the subextremal case we prove that instability results hold for a set of gauge invariant quantities along the event horizon H+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal {H}}^+ $$\\end{document}. In particular, for associated quantities shown to satisfy generalized Regge–Wheeler equations we prove decay, non-decay, and polynomial blow-up estimates asymptotically along H+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal {H}}^+ $$\\end{document}, the exact behavior depending on the number of translation invariant derivatives that we take. As a consequence, we show that for generic initial data, solutions to the generalized Teukolsky system of positive and negative spin satisfy both stability and instability results. It is worth mentioning that the negative spin solutions are significantly more unstable, with the extreme curvature component α̲\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\underline{\\alpha }} $$\\end{document} not decaying asymptotically along the event horizon H+,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal {H}}^+, $$\\end{document} a result previously unknown in the literature.

Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge

We utilize a holographic construction to compute the entanglement negativity for bipartite mixed state configurations of a single subsystem in CFTd s with a conserved charge dual to bulk geometries. In this context, we obtain the holographic entanglement negativity for single subsystems with long rectangular strip geometries in CFTd s with a conserved charge dual to bulk non extremal and extremal Reissner–Nordström (RN)- black holes at the leading order in a perturbation theory. We demonstrate that the holographic entanglement negativity computed involves the elimination of thermal contributions at the leading order confirming earlier results in the literature. This also conforms to quantum information theory expectations and constitutes further consistency checks for the holographic construction.

Hawking temperature as the total Gauss–Bonnet invariant of the region outside a black hole

We provide two novel ways to compute the surface gravity (kappa ) and the Hawking temperature (T_{H}) of a stationary black hole: in the first method T_{H} is given as the three-volume integral of the Gauss–Bonnet invariant (or the Kretschmann scalar for Ricci-flat metrics) in the total region outside the event horizon; in the second method it is given as the surface integral of the Riemann tensor contracted with the covariant derivative of a Killing vector on the event horizon. To arrive at these new formulas for the black hole temperature (and the related surface gravity), we first construct a new differential geometric identity using the Bianchi identity and an antisymmetric rank-2 tensor, valid for spacetimes with at least one Killing vector field. The Gauss–Bonnet tensor and the Gauss–Bonnet scalar play a particular role in this geometric identity. We calculate the surface gravity and the Hawking temperature of the Kerr and the extremal Reissner–Nordström holes as examples.

The Space-Time Properties of Three Static Black Holes

In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy term—the kinetic energy term of the four-dimensional curved space-time. In the case of small space-time curvature, linear approximation can be made. That is, under the weak field approximation, the Lagrangian quantity degenerates into the Lagrangian quantity in the axisymmetric gravitational field in Newtonian mechanics. In this paper, the curved space-time composed of axisymmetric equidistant black holes is taken as a model. We study the geodesic motion of the test particles around three black holes with equal mass and static axisymmetric distribution, including time-like particles and photons. The three extreme Reissner–Nordstrom black holes are balanced by electrostatic and gravitational forces. We first give the geodesic motion equation of particles in Three black holes space-time, give the relativistic effective potential, discuss the possible motion state of particles, and classify their motion trajectories. Then, the particle motion of the special plane (equatorial plane) is studied. The circular orbits of the two types of particles in the symmetric plane are studied, respectively. The circular orbits outside the symmetric plane are also studied, and their stability is also discussed. We will show the influence of the separation distance of the three black holes on the geodesic motion and explore the change of the relativistic effective potential. Then, the relationship between the inherent quantity and the coordinate quantity in space-time is analyzed. Finally, the chaos of the test particle orbit is explored.

No black hole bomb for D-dimensional extremal Reissner–Nordstrom black holes under charged massive scalar perturbation

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 case and prove that there is no black hole bomb for D-dimensional Reissner–Nordstrom black hole under charged massive scalar perturbation and the system is superradiantly stable.

Asymptotic quasinormal frequencies of different spin fields in d-dimensional spherically-symmetric black holes

While Hod’s conjecture is demonstrably restrictive, the link he observed between black hole (BH) area quantisation and the large overtone (n) limit of quasinormal frequencies (QNFs) motivated intense scrutiny of the regime, from which an improved understanding of asymptotic quasinormal frequencies (aQNFs) emerged. A further outcome was the development of the ‘monodromy technique’, which exploits an anti-Stokes line analysis to extract physical solutions from the complex plane. Here, we use the monodromy technique to validate extant aQNF expressions for perturbations of integer spin, and provide new results for the aQNFs of half-integer spins within higher-dimensional Schwarzschild, Reissner–Nordström, and Schwarzschild (anti-)de Sitter BH spacetimes. Bar the Schwarzschild anti-de Sitter case, the spin-1/2 aQNFs are purely imaginary; the spin-3/2 aQNFs resemble spin-1/2 aQNFs in Schwarzschild and Schwarzschild de Sitter BHs, but match the gravitational perturbations for most others. Particularly for Schwarzschild, extremal Reissner–Nordström, and several Schwarzschild de Sitter cases, the application of n → ∞ generally fixes and allows for the unbounded growth of in fixed quantities.

Hidden Killing fields, geometric symmetries and black hole mergers

In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields – so-called hidden Killing vector fields – are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner–Nordström black holes.

Superradiant stability of five and six-dimensional extremal Reissner\u2013Nordstrom black holes

We revisit the superradiant stability of five and six-dimensional extremal Reissner–Nordstrom black holes under charged massive scalar perturbation with a new analytical method. 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. The new method we developed is based on the Descartes’ rule of signs for the polynomial equations. Our result provides a complementary support of previous studies on the stability of higher dimensional extremal Reissner–Nordstrom black holes based on numerical methods.

Quasinormal Modes in Extremal Reissner\u2013Nordstr\xf6m Spacetimes

We present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that L^2-based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce L^2-based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting.

Bending of light and inhomogeneous Picard–Fuchs equation

The bending of light rays by gravitational sources is one of the first evidence of general relativity. When the gravitational source is a stationary massive object such as a black hole, the bending angle has an integral representation, from which various series expansions up to a finite order in terms of the parameters of orbit and the background spacetime has been derived. However, it has not been clear that it has any analytic expansion. In this paper, we show that such an analytic expansion can be obtained for the case of a Schwarzschild black hole by solving an inhomogeneous Picard–Fuchs equation, which has been applied to compute effective superpotentials on D-branes in the Calabi–Yau manifolds. From the analytic expression of the bending angle, the full order expansions in both weak and strong deflection limits are obtained. We show that the result can be obtained by the direct integration approach as well. We also discuss how the charge of the gravitational source affects the bending angle and show that a similar analytic expression can be obtained for the extremal Reissner–Nordström spacetime.

Yang–Mills monopoles in extremal Reissner–Nordström black hole metric

We show that the closed-form monotone solution linking two different vacuum states, for the exterior Yang–Mills wave equation over the extremal Reissner–Nordström spacetime found in the recent work of Bizoń and Kahl [Classical Quantum Gravity 33, 175013 (2016)], is the unique solution to an associated domain-wall type energy minimization problem. We also derive the accompanying interior Yang–Mills wave equation within the same formalism. We obtain a few more closed-form solutions, regular and singular, among other solutions of oscillatory behavior, and discuss several interesting features of the solutions based on some energy considerations.

Characteristic Orbits Of Charged Particles Around Charged Black Holes

We have considered Reissner-Nordstr¨om (RN) charged nonrotating black hole (BH).We have studied motion of charged particles around charged RN BH. It was found out that there are two boundary conditions for specific angular momentum of stable circular orbits corresponding to: innermost stable circular orbits (ISCO) and outermost stable circular orbits (OSCO) and accretion disk is originated between these two orbits. It was obtained the upper and lower limits for the value of particle’s charge which may exist in the accretion disk matter around the extreme charged Reissner Nordstr¨om black hole.

Strong gravity effects of charged Q-clouds and inflating black holes

In this paper, we re-examine charged Q-clouds around spherically symmetric, static black holes. In particular, we demonstrate that for fixed coupling constants two different branches of charged scalar clouds exist around Schwarzschild black holes. This had not been noticed previously. We find that the new solutions possess a ‛hard wall’ at maximal possible gauge coupling. This wall separates the interior (containing the black hole horizon), in which the scalar field is trapped in the ‛false vacuum’, from the ‛true vacuum’ exterior. When taking back-reaction onto the space-time into account, we find that at maximal possible back-reaction, the black hole solutions corresponding to these two branches either become extremal black holes with diverging scalar field derivative on the horizon or inflating black holes with a second, ‛cosmological’ horizon which—outside this second horizon—correspond to extremal Reissner–Nordström black holes.

Test particles dynamics around deformed Reissner-Nordström black hole

In this paper we study the dynamics of neutral, electrically charged and magnetized particles around deformed electrically and magnetically charged Reissner-Nordstr\"om black holes. For the neutral test particles motion, it is shown that the radius of the innermost stable circular orbits (ISCOs) decrease with the increase in both the black hole charge and positive spacetime deformation. It reaches up to $3.85M$ at the value of deformation parameter $\ensuremath{\epsilon}=20.45$ in Schwarzschild spacetime case ($Q=0$). In the extreme charged Reissner--Nordstrom black hole case, the ISCO decreases up to $2.26M$ at the value of deformation parameter $\ensuremath{\epsilon}=6.17$. Moreover, the negative deformation results in an increase in the ISCO radius. Comparing effects of positive deformation and the Reissner-Nordstr\"om black hole charge with spin of rotating Kerr black holes, it is shown that the extremely charged Reissner-Nordstr\"om black hole can mimic rotating Kerr black hole up to the spin parameter $a/M=0.48$, while for the positive deformation with $\ensuremath{\epsilon}=6.17$ the mimic value increases up to $a/M=0.88$ implying that the supermassive black hole M87 cannot be considered as Reissner-Nordstr\"om black hole. Using this comparison, we estimate charge of the supermassive black hole Sagittarius A* as $Q/M\ensuremath{\simeq}0.8287$ without deformation which can mimic the spin of the black hole. When the deformation $\ensuremath{\epsilon}=1$, the mimic charge increases up to $Q/M\ensuremath{\simeq}0.8926$. Our study of the energy extraction from the accretion disk shows that the maximum energy efficiency increases up to 20.02%, which is almost the same for extreme Kerr black hole case (20.6%). We have also considered the behaviour of ISCO of electrically charged particles showing that the attractive (repulsive) electrostatic interactions cause rapid increase (slightly decrease) of the ISCO radius. Finally, we have explored the dynamics of magnetized particles around deformed magnetically charged Reissner-Nordstr\"om black hole. By treating the magnetar PSR J1745-2900, orbiting the supermassive black hole Sagittarius A* as a magnetized particle, showing that the magnetic charge of pure Reissner-Nordstr\"om black hole can mimic spin of a rotating Kerr black hole up to $a/M\ensuremath{\simeq}0.82$ for the value to be in the range ${Q}_{m}/M\ensuremath{\in}(0,0.692)$. Moreover, we find that the positive values of the deformation parameter lead to shift the ISCO for the magnetized particles toward the central object.

Critical Solutions of Scalarized Black Holes

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes.

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.

A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner\u2013Nordstr\xf6m

It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the backwards direction. In this paper, we construct a definitive (bijective) non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström backgrounds. We make use of physical-space energy norms which are non-degenerate both at the event horizon and at null infinity. As an application of our theory we present a construction of a large class of smooth, exponentially decaying modes. We also derive scattering results in the black hole interior region.

Self-gravitating razor-thin discs around black holes via multi-hole seeds

We construct self-gravitating razor-thin discs of counterrotating matter around Schwarzschild black holes (BHs) by applying the ‘displace, cut, and reflect’ method to known seed solutions representing multi-holes. All but one of the sources of the seed solution generate the surrounding annular disc, whereas the remaining BH is mapped onto a Schwarzschild BH which lies at the disc centre after the transformation. The discs are infinite in extent, have annular character, and are linearly stable up to the innermost stable circular orbit (ISCO) of the system. The spacetime is asymptotically flat, having finite Arnowitt–Deser–Misner mass. Moreover, all energy conditions for the disc are satisfied for radii larger than the ISCO radius; the method, however, produces counterrotating streams with superluminal velocities in the vicinity of the central BH. We also comment on charged discs around extremal Reissner–Nordström BHs constructed from a Majumdar–Papapetrou N-BH seed solution. These simple examples can be extended to more general ‘BH + disc’ solutions, obtained by the same method from seeds of the type ‘BH + arbitrary axisymmetric source’. A natural follow-up of this work would be to construct discs around Reissner–Nordström BHs with arbitrary charge-to-mass ratio and around Kerr BHs.

Nonlinear Scalar Perturbations of Extremal Reissner–Nordström Spacetimes

We present the first rigorous study of nonlinear wave equations on extremal black hole spacetimes without any symmetry assumptions on the solution. Specifically, we prove global existence with asymptotic blow-up for solutions to nonlinear wave equations satisfying the null condition on extremal Reissner–Nordstrom backgrounds. This result shows that the extremal horizon instability persists in model nonlinear theories. Our proof crucially relies on a new vector field method that allows us to obtain almost sharp decay estimates.

Late-time asymptotics for the wave equation on extremal Reissner–Nordström backgrounds

We derive the precise late-time asymptotics for solutions to the wave equation on extremal Reissner–Nordström black holes and explicitly express the leading-order coefficients in terms of the initial data. Our method is based on purely physical space techniques. We derive novel weighted energy hierarchies and develop a singular time inversion theory which allow us to uncover the subtle contribution of both the near-horizon and near-infinity regions to the precise asymptotics. We introduce a new horizon charge and provide applications pertaining to the interior dynamics of extremal black holes. Our work confirms, and in some cases extends, the numerical and heuristic analysis of Lucietti–Murata–Reall–Tanahashi, Ori–Sela and Blaksley–Burko.