Extremal Reissner-Nordstrom Black Hole Research Articles

Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS

In the Einstein-Maxwell-charged scalar system with a negative cosmological constant in arbitrary dimensions higher than three, there exists a horizonless charged soliton solution, which we construct explicitly for an arbitrary mass of the scalar in perturbative series in small charge. We find that the stability of the soliton is determined by the validity of the AdS weak gravity conjecture. The existence of a stable soliton might endanger the convexity of the (free) energy as a function of the charge because the phase transition between the soliton and the extremal Reissner-Nordstrom black hole would be discontinuous. We, however, argue that the existence of the hairy black hole solution circumvents the violation of convexity. The thermodynamic properties of the hairy black hole show that the phase transition becomes continuous irrespective of whether the AdS weak gravity conjecture holds. When it holds, the phase transition occurs between the soliton and the hairy black hole, and when it is violated, the phase transition occurs between the extremal Reissner-Nordstrom black hole and the hairy black hole.

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.

Higher-dimensional non-extremal Reissner-Nordstrom black holes, scalar perturbation and superradiance: An analytical study

The superradiant stability of asymptotically flat 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-Nordstrom black holes are also superradiantly stable under charged massive scalar perturbation. Our result implies that all higher dimensional non-extremal Reissner-Nordstrom black holes may be superradiantly stable under charged massive scalar perturbation.

Regular scalar charged clouds around a Reissner-Nordstrom black hole and no-hair theorems

In this work we reanalyze the possibility of finding bound states (scalar clouds) of a test, charged and complex-valued scalar field with mass and charge q in the background of a Reissner-Nordstrom black hole (RNBH). In order to determine the existence of such scalar clouds we impose suitable regularity conditions for the scalar field at the event horizon. We find numerical evidence for the absence of such clouds in the subextremal and extremal RNBH when the field is massive but not self-interacting. More importantly, we put forward a theorem that proves that such clouds cannot exist. On the other hand, when a suitable self-interacting potential is included, the theorem no longer applies, providing a heuristic justification behind the existence of charged clouds (Q-clouds) that were reported recently.

Scattering of gravitational and electromagnetic waves off AdS2 \xd7 S2 in extreme Reissner-Nordstrom

The direct product of two-dimensional anti-de Sitter spacetime with a two-sphere is an exact solution of four-dimensional Einstein-Maxwell theory without a cosmological constant. In this paper, we analytically solve the coupled gravitational and electromagnetic perturbation equations of AdS2 × S2 in Einstein-Maxwell theory. On the other hand, AdS2 × S2 also describes the near-horizon region of the extreme Reissner-Nordstrom (ERN) black hole. We therefore also solve the connection problem: we show how the AdS2 × S2 perturbation equations arise from an appropriate near-horizon approximation of the corresponding equations for the ERN and then, using matched asymptotic expansions, we analytically extend the AdS2 × S2 solutions away from the near-horizon region connecting them with solutions in the far asymptotically flat region. From the point of view of ERN our results may be thought of as computing the classical scattering matrix for gravitational and electromagnetic waves which probe the near-horizon region of the black hole.

Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole

In this paper we employ the results of a previous paper on the late-time decay of scalar-field perturbations of an extreme Reissner-Nordstrom black hole, in order to find the late-time decay of coupled electromagnetic and gravitational perturbations of this black hole. We explicitly write the late-time tails of Moncrief's gauge invariant variables and of the perturbations of the metric tensor and the electromagnetic field tensor in the Regge-Wheeler gauge. We discuss some of the consequences of the results and relations to previous works.

Quasinormal modes of extremal black holes

The continued fraction method (also known as Leaver's method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for neutral massless fields around an extremal Reissner-Nordstrom black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordstrom black hole and to neutral massless perturbations around an extremal Kerr black hole. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed.

Damped and zero-damped quasinormal modes of charged, nearly extremal black holes

Despite recent progress, the complete understanding of the perturbations of charged, rotating black holes as described by the Kerr-Newman metric remains an open and fundamental problem in relativity. In this study, we explore the existence of families of quasinormal modes of Kerr-Newman black holes whose decay rates limit to zero at extremality, called zero-damped modes in past studies. We review the nearly extremal and WKB approximation methods for spin-weighted scalar fields (governed by the Dudley-Finley equation) and give an accounting of the regimes where scalar zero-damped and damped modes exist. Using Leaver’s continued fraction method, we verify that these approximations give accurate predictions for the frequencies in their regimes of validity. In the nonrotating limit, we argue that gravito-electromagnetic perturbations of nearly extremal Reissner-Nordstrom black holes have zero-damped modes in addition to the well-known spectrum of damped modes. We provide an analytic formula for the frequencies of these modes, verify their existence using a numerical search, and demonstrate the accuracy of our formula. These results, along with recent numerical studies, point to the existence of a simple universal equation for the frequencies of zero-damped gravito-electromagnetic modes of Kerr-Newman black holes, whose precise form remains an open question.

Extremal RN/CFT in both hands revisited

We study RN/CFT correspondence for four dimensional extremal Reissner–Nordstrom black hole. We uplift the 4d RN black hole to a 5d rotating black hole and make a geometric regularization of the 5d space–time. Both hands central charges are obtained correctly at the same time by Brown–Henneaux technique.

Microscopic entropy of the magnetised extremal Reissner-Nordstrom black hole

The extremal Reissner-Nordstrom black hole embedded in a Melvin-like magnetic universe is studied in the framework of the Kerr/CFT correspondence. The near horizon geometry can be written as a warped and twisted product of $AdS_2 \times S^2$, also in presence of an axial external magnetic field that deforms the black hole. The central charge of the Virasoro algebra can be extracted from the asymptotic symmetries. Using the Cardy formula for the microscopic statistical entropy of the dual two-dimensional CFT, the Bekenstein-Hawking entropy, for this charged and magnetised black hole, is reproduced.

On Perturbations of Extreme Kerr–Newman Black Holes and their Evolution

Using black hole inequalities and the increase of the horizon’s areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner–Nordstrom black hole that (by contradiction) cannot decay in time into any extreme Kerr–Newman black hole. This proves that, in a formal sense, the reduced family of the extreme Kerr–Newman black holes is unstable. It remains of course to be seen whether the whole family of charged black holes, including those extremes, is stable or not.

Real Scalar Field Scattering Around the Extreme Reissner-Nordström Black Hole in de Sitter Spacetime

The real scalar field scattering of the extreme Reissner-Nordstrom black hole in de Sitter spacetime is investigated numerically via the polynomial approximation. It is found that the scalar field behaves like harmonic waves under the tortoise coordinate, while piles up near the outer event horizon and the cosmological horizon. The abnormity in previous work is eliminated by appropriate application of the boundary conditions in numerical calculations. Substituting the continuous effective potential with a stair potential of n steps, we evaluate the transmission and reflection coefficients of the scalar field in high and low energy regimes, where an asymptotical formula is derived.

Charged dilatonic ads black holes and magnetic AdS D−2 × R 2 vacua

We consider D-dimensional Einstein gravity coupled to two U(1) fields and a dilaton with a scalar potential. We derive the condition that the analytical AdS black holes with two independent charges can be constructed. Turning off the cosmological constant, the extremal Reissner-Nordstrom black hole emerges as the harmonic superposition of the two U(1) building blocks. With the non-vanishing cosmological constant, our extremal solutions contain the near-horizon geometry of AdS_2 x R^{D-2} with or without a hyperscaling. We also obtain the magnetic AdS_{D-2} x Y^2 vacua where Y^2 can be R^2, S^2 or hyperbolic 2-space. These vacua arise as the fix points of some super potentials and recover the known supersymmetric vacua when the theory can be embedded in gauged supergravities. The AdS_{D-2} x R^2 vacua are of particular interest since they are dual to some quantum field theories at the lowest Landau level. By studying the embedding of some of these solutions in the string and M-theory, we find that the M2/M5-system with the equal M2 and M5 charges can intersect with another such M2/M5 on to a dyonic black hole. Analogous intersection rule applies also to the D1/D5-system. The intersections are non-supersymmetric but in the manner of harmonic superpositions.

The Global Structure of Spherically Symmetric Charged Scalar Field Spacetimes

We study the spherical collapse of self-gravitating charged scalar fields. The main result gives a complete characterization of the future boundary of spacetime, providing a starting point for studying the cosmic censorship conjectures. In general, the boundary includes two null components, one emanating from the center of symmetry and the other from the future limit point of null infinity, joined by an achronal component to which the area-radius function r extends continuously to zero. Various components of the boundary a priori may be empty and establishing such generic emptiness would suffice to prove formulations of weak or strong cosmic censorship. As a simple corollary of the boundary characterization, the present paper rules out scenarios of ‘naked singularity’ formation by means of ‘super-charging’ (near-)extremal Reissner-Nordstrom black holes. The main difficulty in delimiting the boundary is isolated in proving a suitable global extension principle that effectively excludes a broad class of singularity formation. This suggests a new notion of ‘strongly tame’ matter models, which we introduce in this paper. The boundary characterization proven here extends to any such ‘strongly tame’ Einstein-matter system.

Area Spectra of d-Dimensional Extreme Reissner-Nordström Black Holes

With the physical interpretation of quasinormal modes proposed by Maggiore, we investigate the quantum area and entropy spectra of d-dimensional extreme Reissner-Nordstrom black holes. Employing two methods, the method of Maggiore and the action variable quantization, we arrive at the spectra consistent with each other. Results show that the spectra are irrelevant to the black hole parameters and the perturbation field parameters but relative to the spacetime dimension. For a given dimension, the spectra are equally spaced.

Near horizon geometry, Brick wall model and the Entropy of a scalar field in the Reissner-Nordstrom black hole backgrounds

In this article we will find the entropy of a scalar field in the Reissner-Nordstrom black hole backgrounds using the brick wall model of t' Hooft. We will use the semi-classical WKB approximation. We will consider the modes which are globally stationary so that the WKB quantization rule used in the brick wall model remains valid. In the Schwarzschild black hole this consideration had led to a new expression of the entropy different from the conventional expression which is inversely divergent in the brick wall cut-off parameter and in terms of a proper distance cut-off parameter, is proportional to the area of the event horizon. The new expression of the scalar field entropy obtained in this article is logarithmically divergent in the brick wall cut-off parameter and is not proportional to the area of the black hole event horizon. For the extremal Reissner-Nordstrom black hole background the entropy of the scalar field is again divergent in the brick wall cut-off parameter and vanishes if the temperature of the Hawking radiation and the black hole is taken to be zero. We will next consider the entropy for a thin shell of matter field surrounding the black hole horizon. When expressed in terms of a covariant cut-off parameter, the entropy of a thin shell of matter field surrounding the horizon in the non-extreme Reissner-Nordstrom black hole background is given by an expression proportional to the area of the black hole horizon. We will briefly explain the significance of this result.

Quantum field theory on the Bertotti-Robinson space-time

We consider the problem of quantum field theory on the Bertotti-Robinson space-time, which arises naturally as the near horizon geometry of an extremal Reissner-Nordstrom black hole but can also arise in certain near-horizon limits of non-extremal Reissner Nordstrom space-time. The various vacuum states have been considered in the context of $AdS_{2}$ black holes by Spradlin and Strominger who showed that the Poincare vacuum, the Global vacuum and the Hartle-Hawking vacuum are all equivalent, while the Boulware vacuum and the Schwarzschild vacuum are equivalent. We verify this by explicitly computing the Green's functions in closed form for a massless scalar field corresponding to each of these vacua. Obtaining a closed form for the Green's function corresponding to the Boulware vacuum is non-trivial, we present it here for the first time by deriving a new summation formula for associated Legendre functions that allows us to perform the mode-sum. Having obtained the propagator for the Boulware vacuum, which is a zero-temperature Green's function, we can then consider the case of a scalar field at an arbitrary temperature by an infinite image imaginary-time sum, which yields the Hartle-Hawking propagator upon setting the temperature to the Hawking temperature. Finally, we compute the renormalized stress-energy tensor for a massless scalar field in the various quantum vacua.

Tunneling between single- and multicentered black hole configurations

We find a gravitational instanton that connects an initial state corresponding to a single-centered extremal Reissner-Nordstrom black hole configuration, to a final state corresponding to a multicentered configuration. This instanton is interpreted as describing quantum tunneling between the two different black hole solutions. We evaluate the Euclidean action for this instanton and find that the amplitude for the tunneling process is equal to half the difference in entropy between the initial and final configurations.

Spectroscopies of Extreme Black Holes

The spectroscopies of extreme black holes are investigated by the intrinsic property of these black holes in this paper. We find that the area spectrum of the extreme Reissner-Nordstrom black hole is dependent on the fine structure constant. While the area spectra share the same expression and are determined by the quantum numbers of angular momentum for the extreme Kerr-Sen Dilaton-Axion and Kaluza-Klein black holes.