Reissner-Nordstrom Research Articles

Thick Shell Evolution in Reissner–Nordstr?m Spacetime

The new extension formalism, developed by Khakshournia and Mansouri, is used to analyze the dynamics of a general shell of matter with an arbitrary finite thickness immersed in a curved space time. Within this new formulation the equations of motion of a spherically symmetric thick shell immersed in Reissner–Nordström (RN) space time is obtained.

Black-hole Solution Without Curvature Singularity and Closed Timelike Curves

With a prescribed Coulomb-type energy-momentum tensor, an exact solution of the Einstein field equations over a nonsimply-connected manifold is presented. This spherically symmetric solution has neither curvature singularities nor closed timelike curves. It can be considered to be a regularization of the singular Reissner-Nordstrom solution over a simply-connected manifold.

Static spherically symmetric solution of the Einstein-aether theory

By using the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an inner Cauchy horizon and an outer black hole event horizon. But a remarkable difference from the Reissner-Nordstrom solution is that it is not asymptotically flat but approaches a two-dimensional sphere. The resulting electric potential is regular in the whole spacetime except for the curvature singularity. On the other hand, the magnetic potential is divergent on both the Cauchy horizon and the outer event horizon.

The structure of the integral of motion for a charged body in the relativistic theory of gravitation

The energy-momentum tensor in the relativistic theory of gravitation (RTG) is calculated for the Reissner-Nordstrom metric. The external gravitational energy of a collapsing body is found. Based on an analysis of its behavior near a gravitational radius, it is concluded that gravitational collapse is impossible.

Geometrodynamics of a thin shell in the Reissner-Nordström metric

The geometrodynamics of a thin, dust, electrically neutral shell in the metric of a charged Reissner-Nordstrom black hole is considered. The Arnowitt-Deser-Misner formalism is used to construct the thin-shell Hamiltonian. The wave equation is derived. The wave equation is shown to be a second-order homogeneous difference equation. Exact analytical solutions have been found.

What happens at the horizon(s) of an extreme black hole?

A massless scalar field exhibits an instability at the event horizon of an extreme black hole. We study numerically the nonlinear evolution of this instability for spherically symmetric perturbations of an extreme Reissner–Nordstrom (RN) black hole. We find that generically the endpoint of the instability is a non-extreme RN solution. However, there exist fine-tuned initial perturbations for which the instability never decays. In this case, the perturbed spacetime describes a time-dependent extreme black hole. Such solutions settle down to extreme RN outside, but not on, the event horizon. The event horizon remains smooth but certain observers who cross it at late time experience large gradients there. Our results indicate that these dynamical extreme black holes admit a C1 extension across an inner (Cauchy) horizon.

Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime

A charged scalar field impinging upon a charged Reissner-Nordstrom black hole can be amplified as it scatters off the hole, a phenomenon known as superradiant scattering. This scattering process in the superradiant regime w<qQ/r_+ (here w, q, Q, and r_{+-} are the conserved frequency of the wave, the charge coupling constant of the field, the electric charge of the black hole, and the horizon radii of the black hole, respectively) results in the extraction of Coulomb energy and electric charge from the charged black hole. The black-hole-field system can be made unstable by placing a reflecting mirror around the black hole which prevents the amplified field from escaping to infinity. This charged black-hole-mirror system is the spherically symmetric analogue of the rotating black-hole-mirror bomb of Press and Teukolsky. In the present paper we study analytically the charged black-hole-mirror bomb in the asymptotic regime qQ>>1 and for mirror radii r_m in the near-horizon region x_m=(r_m-r_+)/r_+<<tau, where tau=(r_+-r_-)/r_+ is the dimensionless temperature of the black hole. In particular, we derive analytic expressions for the oscillation frequencies w_R and the instability growth timescales 1/w_I of the superradiant confined fields. Remarkably, we find a simple linear scaling w_I \propto qQ/r_+ for the imaginary part of the resonances in the asymptotic qQ>>(tau/x_m)^2>>1 regime, which implies that the instability timescale 1/w_I of the system can be made arbitrarily short in the qQ-->infinity limit. The short instability timescale found in the linear regime along with the spherical symmetry of the system, make the charged bomb a convenient toy model for future numerical studies aimed to investigate the non-linear end-state of superradiant instabilities.

Entropy of Non-stationary and Slowly Changing Reissner-Nordström Black Hole

Simplifying Dirac equation near the horizon, Hawking temperature is obtained by applying a new tortoise coordinate transformation. Using the improved thin film brick-wall model and WKB approximation, the entropy of Dirac field in the non-stationary and slowly changing Reissner-Nordstrom black hole is calculated. The result shows that the entropy of the black hole is still proportional to the horizon area, and black hole entropy is just identical to the entropy of the quantum state at the horizon. In addition, the new tortoise coordinate transformation can make the cut-off parameter introduced in solving the entropy of non-stationary black hole simplified to the same as that in the static and stationary cases.

Emergent Schwarzschild and Reissner-Nordstrom black holes in four dimensions: An effective curvature sourced by aB2-field on aD4-brane

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.

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.

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

In the tunneling framework of Hawking radiation, charged particle’s tunneling in the modified Reissner-Nordstrom black hole from gravity’s rainbow is investigated. To this end, following the Schwarzschild solution in gravity’s rainbow, the metric of the modified Reissner-Nordstrom black hole is given. In the tunneling process, the metric fluctuation is taken into account, due to not only the energy conservation and electric charge conservation, but also the spacetime quantum effects. The calculation shows out that the emission rate satisfies the first law of black hole thermodynamics and is consistent with an underlying unitary theory. In addition, it is found that the entropy of the modified black hole is different to the Benkestein-Hawking entropy and the quantum corrections of the entropy appears.

Entropy-product rules for charged rotating black holes

We study the universal nature of the product of the entropies of all horizons of charged rotating black holes. We argue, by examining further explicit examples, that when the maximum number of rotations and/or charges are turned on, the entropy product is expressed in terms of angular momentum and/or charges only, which are quantized. (In the case of gauged supergravities, the entropy product depends on the gauge-coupling constant also.) In two-derivative gravities, the notion of the "maximum number" of charges can be defined as being sufficiently many non-zero charges that the Reissner-Nordstrom black hole arises under an appropriate specialisation of the charges. (The definition can be relaxed somewhat in charged AdS black holes in $D\ge 6$.) In higher-derivative gravity, we use the charged rotating black hole in Weyl-Maxwell gravity as an example for which the entropy product is still quantized, but it is expressed in terms of the angular momentum only, with no dependence on the charge. This suggests that the notion of maximum charges in higher-derivative gravities requires further understanding.

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.

Hot plasma waves in Veselago medium around Reissner-Nordström black hole

We investigate the general relativistic magnetohydronadynamic (GRMHD) equations for hot plasmas in a Veselago medium around the Reissner-Nordstrom (RN) black hole. Using the 3+1 formalisms of spacetime, we write the GRMHD equations and perturb them linearly. These are then Fourier analyzed for the magnetized and nonmagnetized plasmas in rotating and nonrotating backgrounds. We derive dispersion relations and analyze the wave properties by the graphs of wave vector, refractive index and change in refractive. The results confirm the presence of Veselago medium for rotating magnetized/nonmagnetized and nonrotating nonmagnetized plasmas.

Tunneling of massive and charged particles from noncommutative Reissner-Nordström black hole

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 this setup.

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordstrom black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.

BOUNDING THE GREYBODY FACTORS FOR NON-ROTATING BLACK HOLES

Semiclassical black holes emit radiation called Hawking radiation. Such radiation, as seen by an asymptotic observer far outside the black hole, differs from the original radiation near the horizon of the black hole by a redshift factor and the so-called "greybody factor." In this paper, we concentrate on the greybody factor; various bounds for the greybody factors of non-rotaging black holes are obtained, concentrating primarily on charged Reissner–Nordström (RN) and RN–de Sitter black holes. These bounds can be derived using a 2 × 2 transfer matrix formalism. It is found that the charges of black holes act as efficient barriers. Furthermore, adding extra dimensions to spacetime can shield Hawking radiation. Finally, it is also found that the cosmological constant can increase the emission rate of Hawking radiation.

STABLE AND DECAYING BOUND STATES ON THE NAKED REISSNER–NORDSTRÖM SPACETIME

We present a quantum mechanical study of the bound states of a neutral scalar particle on the curved background described by the Reissner–Nordström (RN) spacetime that corresponds to a naked singularity. We show that there occurs both the metastable, i. e. decaying bound states and the stable ones. The corresponding energy spectra are calculated in the leading WKB approximation and the comparison with RN black hole quasinormal mode spectrum is made. The metastable bound states on the naked singularity background turn out to be more long-living than the quasinormal modes for the black hole with the same mass.

A two-point boundary-value problem for gyroscopic systems in some Lorentzian manifolds

We study the dynamics of gyroscopic systems of relativistic type with multivalued action functionals. We assume that Lorentzian configuration manifolds have the structure of the twisted product. The solvability of the two-point boundary-value problem for such systems was proved earlier only in the case of a limited Lorentzian distance from the initial point to the final one. In this work we obtain a new existence theorem. According to this theorem, the specified distance to attainable points may be arbitrarily large. The result is applied to the dynamics of a charged test particle in the external space-time of the Reissner-Nordstrom black hole.

Isotropic Reissner-Nordström Geometry and the Corresponding Gravitational Redshift

In this letter, we first consider the famous non-vacuum solution of general relativity for a static spherically symmetric charged object, i.e. the Reissner-Nordstrom solution. Afterwards, by adopting an isotropic coordinate system, we derive the equivalent form of this solution in the so-called geometry. Then we discuss the gravitational redshift in the consequent spacetime.