Reissner-Nordstrom Research Articles

Gravitational lensing of stars orbiting Sgr A* as a probe of the black hole metric in the Galactic center

We show that a possible astrophysical experiment, detection of lensed images of stars orbiting close to Sgr A*, can provide insight into the form of the metric around a black hole. We model Sgr A* as a black hole and add in a $\frac{1}{r^2}$ term to the Schwarzschild metric near the black hole. We then attempt to determine the effect of this extra term on the properties of the secondary images of the S stars in the Galactic Center. When the $\frac{1}{r2}$ term is positive, this represents a Reissner-Nordstrom (RN) metric, and we show that the there is little observational difference between a Schwarzschild black hole and a RN black hole, leading to the conclusion that secondary images may not be a useful probe of electrical charge in black holes. A negative value for the $\frac{1}{r^2}$ term can enter through modified gravity scenarios. Although physically unlikely to apply in the case of a large black hole, the Randall-Sundrum II braneworld scenario admits a metric of this form, known as tidal Reissner- Nordstrom (TRN) metric. We use values of tidal charge (Q in $\frac{Q}{r^2}$) ranging from $-1.6M^2$ to $0.4 M^2$. A negative value of Q enhances the brightness of images at all times and creates an increase in brightness of up to 0.4 magnitudes for the secondary image of the star S2 at periapse. We show that for other stars with brighter secondary images and positions more aligned with the optic axis, using the Tidal Reissner-Nordstrom metric with negative Q enhances the images as well, but the effect is less pronounced. With the next generation of instruments and increased knowledge of radiation from Sgr A*, using properties of secondary images to place constraints on the size of the $\frac{1}{r^2}$ term. This knowledge will be useful in constraining any modified gravity theory that adds a similar term into the strong field near a black hole.

Corrected Hawking Tunneling Radiation in the Higher Dimensional Reissner-Nordström Black Hole

Based on the generalized uncertainty principle, in which the quantum gravitational effects are properly taken in to account, the corrected Bekenstein-Hawking entropy of the higher dimensional Reissner-Nordstrom black hole, up to the square order of Planck length, has been calculated. Using the corrected entropy, the black hole radiation probability has been calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and a generalized quantum tunneling through the event horizon of the black hole is obtained.

Thermal Radiation of Reissner-Nordström Black Hole

By the entropy density near the event horizon, the result has been obtained that the thermal radiation of the black hole satisfies the generalized Stenfan-Boltzmann law. The derived generalized Stenfan-Boltzmann coefficient is no longer a constant, but a proportional coefficient related to the black hole mass, the black hole charge, the average radial effusion velocity of the radiation particles near the event horizon, the cut-off distance and the thin film thickness. For an extreme Reissner-Nordstrom black hole, radiation energy flux and radiation power are all equal to zero. Then, the generalized Stenfan-Boltzmann law will lead to a black hole remnant. In this paper, we have put forward a thermal particle model in curved space-time. By this model, the thermal radiation of the Reissner-Nordstrom black hole has been studied. The result shows that when the thin film thickness and the cut-off distance are both fixed for the Reissner-Nordstrom black hole, the radiation energy flux received by observer far away from the Reissner-Nordstrom black hole is proportional to the average radial effusion velocity of the radiation particles, and inversely proportional to the square of the distance between the observer and the black hole.

Foliation of the Kottler–Schwarzschild–de Sitter spacetime by flat spacelike hypersurfaces

There exist Kruskal like coordinates for the Reissner–Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non-existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler–Schwarzschild–de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.

LOCAL FREE-FALL TEMPERATURE OF A RN–AdS BLACK HOLE

We use the global embedding Minkowski space geometries of a (3+1)-dimensional curved Reissner–Nordström (RN)–AdS black hole space–time into a (5+2)-dimensional flat space–time to define a proper local temperature, which remains finite at the event horizon, for freely falling observers outside a static black hole. Our extended results include the known limiting cases of the RN, Schwarzschild–AdS and Schwarzschild black holes.

Physics of the interior of a black hole with an exotic scalar matter

We use a numerical code to consider the nonlinear processes arising when a Reissner-Nordstrom black hole is irradiated by an exotic scalar field (modelled as a free massless scalar field with an opposite sign for its energy-momentum tensor). These processes are quite different from the processes arising in the case of the same black hole being irradiated by a pulse of a normal scalar field. In our case, we did not observe the creation of a spacelike strong singularity in the T-region of the space-time. We investigate the antifocusing effects in the gravity field of the exotic scalar field with the negative energy density and the evolution of the mass function. We demonstrate the process of vanishing of the black hole when it is irradiated by a strong pulse of an exotic scalar field.

Semiclassical Loop Quantum Black Hole

In this paper we have improved the semiclassical analysis of loop quantum black hole (LQBH) in the conservative approach of constant polymeric parameter. In particular we have focused our attention on the space-time structure. We have introduced a very simple modification of the spherically symmetric Hamiltonian constraint in its holonomic version. The new quantum constraint reduces to the classical constraint when the polymeric parameter goes to zero.Using this modification we have obtained a large class of semiclassical solutions parametrized by a generic function of the polymeric parameter. We have found that only a particular choice of this function reproduces the black hole solution with the correct asymptotic flat limit. In r=0 the semiclassical metric is regular and the Kretschmann invariant has a maximum peaked in L-Planck. The radial position of the pick does not depend on the black hole mass and the polymeric parameter. The semiclassical solution is very similar to the Reissner-Nordstrom metric. We have constructed the Carter-Penrose diagrams explicitly, giving a causal description of the space-time and its maximal extension. The LQBH metric interpolates between two asymptotically flat regions, the r to infinity region and the r to 0 region. We have studied the thermodynamics of the semiclassical solution. The temperature, entropy and the evaporation process are regular and could be defined independently from the polymeric parameter. We have studied the particular metric when the polymeric parameter goes towards to zero. This metric is regular in r=0 and has only one event horizon in r = 2m. The Kretschmann invariant maximum depends only on L-Planck. The polymeric parameter does not play any role in the black hole singularity resolution. The thermodynamics is the same.

CHARGED BLACK HOLES IN VAIDYA BACKGROUNDS: HAWKING'S RADIATION

In this paper we propose a class of embedded solutions of Einstein's field equations describing nonrotating Reissner–Nordstrom–Vaidya and rotating Kerr–Newman–Vaidya black holes. The Reissner–Nordstrom–Vaidya is obtained by embedding Reissner–Nordstrom solution into the nonrotating Vaidya. Similarly, we also find the Kerr–Newman–Vaidya black hole, when Kerr–Newman embeds into the rotating Vaidya solution. The Reissner–Nordstrom–Vaidya solution is type D whereas the Kerr–Newman–Vaidya metric is algebraically special of type II by the Petrov classification of space–time. These embedded solutions can be expressed in the Kerr–Schild ansatze on different backgrounds. The energy–momentum tensors for both nonrotating as well as rotating embedded solutions satisfy the energy conservation equations which show that they are solutions of Einstein's field equations. The surface gravity, area, temperature and entropy are also presented for each embedded black hole. It is observed that the area of the embedded black holes is greater than the sum of the areas of the individual ones. By considering the charge to be a function of radial coordinates it is shown that there is a change in the masses of the variably charged black holes. If such radiation continues, the mass of the black hole will evaporate completely thereby forming "instantaneous" charged black holes and creating embedded negative mass naked singularities describing the possible the life of radiation embedded black holes during their continuous radiation processes.

Noncommutative Inspired Reissner–Nordström Black Holes in Large Extra Dimensions

Recently, a new noncommutative geometry inspired solution of the coupled Einstein–Maxwell field equations including black holes in 4-dimension is found. In this paper, we generalize some aspects of this model to the Reissner–Nordström (RN) like geometries with large extra dimensions. We discuss Hawking radiation process based on noncommutative inspired solutions. In this framework, existence of black hole remnant and possibility of its detection in LHC are investigated.

The RN/CFT correspondence

Recently it has been shown in [S.M. Carroll, et al., arXiv:0901.0931 [hep-th]] that the approach to extremality for the non-extremal Reissner–Nordstrom black hole is not continuous. The non-extremal RN black hole splits into two spacetimes at the extremality: an extremal black hole and a disconnected AdS2×S2 space which has been called the “compactification solution”. As a possible resolution for understanding the entropy of extremal RN black hole, it has been speculated that the entropy of the non-extremal black hole may be carried by the latter solution. By uplifting the four-dimensional “compactification solution” with electric charge Qe to a five-dimensional solution, we show that this solution is dual to a CFT with central charge c=6Qe3. The Cardy formula then shows that the microscopic entropy of the CFT is the same as the macroscopic entropy of the “compactification solution”.

Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime

We study Einstein-Maxwell-dilaton gravity models in four-dimensional antide Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a Lifshitz scaling symmetry. We discuss the optical conductivity in the new dual phase and find interesting behavior at low frequencies where it shows a “Drude peak”. The resistivity varies with temperature in a non-monotonic way and displays a minimum at low temperatures which is reminiscent of the celebrated Kondo effect.

TOPOLOGICAL BLACK HOLES OF EINSTEIN–YANG–MILLS DILATON GRAVITY

We present the topological solutions of Einstein dilaton gravity in the presence of a non-Abelian Yang–Mills field. In four dimensions, we consider the So(3) and So(2, 1) semisimple group as the Yang–Mills gauge group, and introduce the black hole solutions with spherical and hyperbolic horizons, respectively. The solution in the absence of dilaton potential is asymptotically flat and exists only with a spherical horizon. Contrary to the nonextreme Reissner–Nordstrom black hole, which has two horizons with a timelike and avoidable singularity, here the solution may present a black hole with a null and unavoidable singularity with only one horizon. In the presence of dilaton potential, the asymptotic behavior of the solutions is neither flat nor anti–de Sitter. These solutions contain a null and avoidable singularity, and may present a black hole with two horizons, an extreme black hole or a naked singularity. We also calculate the mass of the solutions through the use of a modified version of the Brown–York formalism, and consider the first law of thermodynamics.

DECAY OF MASSLESS DIRAC FIELD AROUND THE BORN–INFELD BLACK HOLE

In this paper we investigate the perturbations by a massless Dirac spinor of a Born–Infeld black hole. The decay rates of the spinor field which is given by the quasinormal mode frequencies are computed using the sixth-order WKB approximation. The behavior of the quasinormal modes with the nonlinear parameter, temperature and charge of the black hole are analyzed in detail. We also compare the decay rates of the Born–Infeld black hole with its linear counterpart Reissner–Nordstrom black hole.

Accretion of exotic matter onto a Reissner-Nordström black hole

The physical processes that arise when exotic matter accretes onto a charged Reissner-Nordstrom black hole are considered. Exotic matter is chosen in the form of dust with a negative mass. The various types of horizons and throats that arise in the accretion process are considered. The Einstein equations are integrated analytically by taking into account the contributions from various types of matter (dust and magnetic field). The derived expressions are reduced to a form convenient for their analytical study. Particular solutions of the system are found for a certain class of initial conditions and constraints related to the possibility of dust-layer intersection are investigated. A fundamental change in solution characteristics related to the possibility of black-hole disappearance is found.

Phase transition in the Reissner–Nordström black hole

The thermodynamics of the Reissner–Nordstrom black hole at the charge-to-mass ratio of \(\sqrt{3}/2\) is studied. We show that there exists infinite discontinuity not only in the heat capacity but also in the electromagnetic potential and hence in the Gibbs free energy. Despite the existence of an infinite discontinuity in the heat capacity, it is shown that there exists no phase transition in the Reissner–Nordstrom black hole. The discontinuity may be merely an artefact of the change in the slope of the |Q| vs. M curve when the charge-to-mass ratio crosses \(\sqrt{3}/2\) . This may signify that the horizon temperature is not a well-behaved thermodynamic parameter in the black hole thermodynamics.

Entropy correction of charged black hole via fermions tunneling beyond semi-classical approximation

Motivated by the idea of tunneling beyond semi-classical approximation of Majhi et al., we discuss entropy correction of Dirac particles tunneling from the Reissner-Nordstrom black hole with a global monopole. To get the corrections correctly, we regard the proportionality constants of quantum correction terms to the semi-classical term of action as the inverse of the square of the Planck Length but not that of the Planck Mass. Our study shows that corrections to the Bekenstein-Hawking entropy, namely the logarithmic term and the inverse area term, may be reproduced as the quantum effect is considered.

The RN/CFT correspondence revisited

We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstr{\o}m black hole in the viewpoint of the AdS$_2$/CFT$_1$ correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is $6 Q^2$ which is different from the previous result $6 Q^3$ of left moving sector obtained by warped AdS$_3$/CFT$_2$ description. We discussed the discrepancy in these two approaches and examined novel properties of our result.

The nuts and bolts of Einstein-Maxwell solutions

We find new non-supersymmetric solutions of five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are regular, horizonless and have the same asymptotic charges as non-extremal charged black holes. An essential ingredient in our construction is a four-dimensional Euclidean base which is a solution to Einstein-Maxwell equations. We construct stationary solutions based on the Euclidean dyonic Reissner-Nordstrom black hole as well as a six-parameter family with a dyonic Kerr-Newman-NUT base. These solutions can be viewed as compactifications of eleven-dimensional supergravity on a six-torus and we discuss their brane interpretation.

AN ANSWER TO THE MAIN BLACK HOLE PATHOLOGY: FORMING NONSINGULAR BLACK HOLES FROM DUST COLLAPSE

The dynamics of gravitational collapse is examined in the realm of string-based formalism of D-branes which encompasses general relativity as a low energy limit. A complete analytical solution is given to the spherically symmetric collapse of a pure dust star, including its matching with a corrected Schwarzschild exterior space–time. The collapse forms a black hole (an exterior event horizon) enclosing not a singularity but perpetually bouncing matter in the infinite chain of space–time maximal analytical extensions inside the outer event horizon. This chain of analytical extensions has a structure analogous to that of the Reissner–Nordstrom solution. The interior trapped bouncing matter has the possibility of being expelled by disruptive nonlinear resonance mechanisms.

INTERSECTIONS OF SELF-GRAVITATING CHARGED SHELLS IN A REISSNER–NORDSTROM FIELD

We describe the equation of motion of two charged spherical shells with tangential pressure in the field of a central Reissner–Nordstrom (RN) source. We solve the problem of determining the motion of the two shells after the intersection by solving the related Einstein–Maxwell equations and by imposing a physical continuity condition on the shells' velocities. In addition, we consider four applications: post-Newtonian and ultrarelativistic approximations, a test-shell case, and the ejection mechanism of one shell. This work is a direct generalization of Barkov–Belinski–Bisnovati–Kogan paper.