Discreteness of Dyonic Dilaton Black Holes

We show that there are two classes of solutions describing static spherically symmetric dyonic dilaton black holes with two nonsingular horizons. The first class includes only the already known solutions that exist for a few special values of the dilaton coupling constant. Solutions in the second class have essentially different properties. They exist for continuously varying values of the dilaton coupling constant but arise only for discrete values of the dilaton field at the horizon. For each given value of the dilaton coupling constant, there can exist several such solutions differing by the number of zeros of the shifted dilaton function in the subhorizon region and separating the domains of singular solutions.     

Effect of interconvertibility of electromagnetic and gravitational waves in strong external electromagnetic fields and the propagation of waves in the field of a charged “black hole” : PMM vol. 38, n 6, 1974, pp. 1122–1129

It is shown that the behavior of an arbitrary wave propagating in the field of a nonrotating charged black hole is defined (with the use of quadratures) by four functions. Each of these functions obeys its second order equation of the wave kind. Short electromagnetic waves falling onto a black hole are reflected by its field in the form of gravitational and electromagnetic waves whose amplitude was explicitly determined. In the case of the wave carrying rays winding around the limit cycle the reflection and transmission coefficients were obtained in the form of analytic expressions.Various physical processes taking place inside, as well as outside a collapsing star, may induce perturbations of the gravitational, electromagnetic and other fields, and lead to the appearance in the surrounding space of waves of various kinds which propagate over a distorted background and are dissipated along its inhomogeneities.In the absence of rotation and charge in a star, the analysis of small perturbations of the gravitational fields is based on the system of Einstein equations linearized around the Schwarzschild solution. In [1, 2] this system of equations, after expansion of perturbations in spherical harmonics and Fourier transformation with respect to time, was reduced to two independent linear ordinary differential equations of second order of the form of the stationary Schrödinger equation for a particle in a potential force field. Each of these equations defines one of two possible independent perturbation kinds: “even” and “odd” (the different behavior of spherical tensor harmonics at coordinate inversion is the deciding factor in the determination of the kind of perturbation [1, 2]). Although these equations were derived with the superposition on the perturbations of the metric of specific coordinate conditions, they define, as shown in [4], the behavior of invariants of the perturbed gravitational field, which imparts to the potential barriers appearing in these equations an invariant meaning.The system of Maxwell equations on the background of Schwarzschild solution also reduces to similar equations, which differ from the above only by the form of potential barriers appearing in these [5].In the presence in the unperturbed solution of a strong electromagnetic field the gravitational and electromagnetic waves interact with each other, and transmutation takes place. The train of short periodic electromagnetic waves generates the accompanying train of gravitational waves. This phenomenon was first analyzed in [6] on and arbitrary background. It was shown in [7, 8] that dense stars surrounded by hot plasma may acquire a charge owing to splitting of charges by radiation pressure and the “sweeping out” of positrons nascent in vapors in strong electrostatic fields. The interaction of waves becomes particularly clearly evident in the neighborhood of black holes which may serve as “valves” by maintaining equilibrium between the relict electromagnetic and gravitational radiation in the Universe. Rotation of black holes intensifies this effect [6].If a nonrotating star possesses an electrostatic charge, the definition of perturbations of the electromagnetic and gravitational fields must be based on the complete system of Einstein-Maxwell equations linearized around the Nordström-Reissner solution. (Small perturbations of electromagnetic field outside a charged black hole were considered in [9, 10] on the basis of the system of Maxwell equations on a “rigid” background of the Nordström-Reissner solution, without taking into account the interconvertibility of gravitational and electromagnetic waves, which materially affects their behavior in the neighborhood of a charged black hole). Here this system of equations which define the interacting gravitational and electromagnetic perturbations are reduced to four independent second order differential equations, two for each kind of perturbations (an importsnt part is played here by the coordinate conditions imposed on the perturbations of the metric, proposed by the authors in [4]). Perturbation components of the metric and of the electromagnetic field are determined in quadratures by the solutions of these equations. If the charge of a star tends to vanish, two of the derived equations convert to equations for gravitational waves on the background of the Schwarzschild solution [1, 2], while the twoothers become equations which are equivalent to Maxwell solutions on the same background. The short-wave asymptotics of derived equations is determined throughout including the neighborhood of the limit cycle for the wave carrying rays. These solutions far away from the point of turn coincide with those obtained in [6] for any arbitrary background. Approximation of geometric optics does not provide correct asymptotics for impact parameters of rays which are close to critical for which the Isotropie and geodesic parameters wind around the limit cycle. This case is investigated below.A similar situation in the Schwarzschild field was analyzed in [11], where analytic expressions for the wave reflection and transmission coefficients were determined, and the integral radiation stream trapped by a black hole produced by another radiation component of the dual system was calculated.     

Entropy of open quantum systems and the Poisson distribution

The entropies of a harmonic oscillator and a quantum Klein-Gordon-Fock field with a static source are found in the coherent state. In both cases, the obtained expressions coincide up to a numerical factor with the Bekenstein-Hawking entropy for a black hole or, more precisely, for the physical vacuum around the hole. Such a coincidence and the property of a gravitational field to make a quantum system placed in this field decoherent lead to the assumption that the vacuum in the vicinity of a black hole is in a coherent state. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 107–115, April, 2000.     

Multidimensional cosmological solutions of the Friedman type in dilaton gravity

Generalized Friedman-type cosmological solutions (spatially homogeneous and isotropic) are obtained and classified in a D-dimensional dilaton gravitational model with the central charge deficit A. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 163–176, April, 2000.     

Thermodynamic quantities around a charged dilaton black hole

We use the brick-wall method to investigate the thermodynamic quantities around a charged dilaton black hole. We show that all the thermodynamic quantities contain two terms: the first term has exactly the same form as in a flat space-time, but the second term depends explicitly on the spin of the fields and therefore cannot be neglected. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 154–160, October, 2008.     

Tunneling radiation of a Gibbons-Maeda dilaton black hole

We use the Parikh-Wilczek method to treat Hawking radiation as a tunneling process across the event horizon and calculate the emission rate of a Gibbons-Maeda dilaton black hole. We show that if self-gravitation is taken into account, then the radiation deviates from the purely thermal spectrum, and the corrected spectrum is consistent with an underlying unitary theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 172–175, April, 2007.     

The Solutions of the Coupled Einstein-Maxwell Equations and Dilaton Equations

In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.     

Integrability of Generalized (Matrix) Ernst Equations in String Theory

We elucidate the integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric (d×d)-matrix Ernst potentials. These equations arise in string theory as the equations of motion for the truncated bosonic parts of the low-energy effective action for the respective dilaton and d×d matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, a U(1) gauge vector field, and an antisymmetric 3-form field, all depending on only two space-time coordinates. We construct the corresponding spectral problems based on the overdetermined 2d×2d linear systems with a spectral parameter and the universal (i.e., solution-independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed existence conditions for each of these systems of two matrix integrals with appropriate symmetries provide specific (coset) structures of the related matrix variables. We prove that these spectral problems are equivalent to the original field equations, and we envisage an approach for constructing multiparametric families of their solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 214–225, August, 2005.     

Elliptic equations governing extremely charged cosmological dust coupled with the dilaton

In this paper, we consider the coupled Einstein and Maxwell equations which are also coupled to a dilaton field in the framework of general relativity. Within the Majumdar–Papapetrou framework, for the static Einstein–Maxwell equations with charged dust as the external source of the fields, one can reduce the electrovacuum field equations into the Poisson equation in the flat space. By using the sub-supersolution method and an energy method, we establish a series of existence theorems for the solutions of this important gravitational system.     

Impossibility of gravitational collapse

In the framework of the relativistic theory of gravity, we show that a universal mechanism for stopping the process of gravitational compression of a body with large mass with its subsequent radial expansion appears because of the gravitational field tensor. This excludes the gravitational collapse and the possibility of black hole formation.     

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

The propagation of a spherical shock wave in a non‐ideal gas with or without gravitational effects is investigated under the action of monochromatic radiation. Similarity solutions are obtained for adiabatic flow between the shock and the piston. The numerical solutions are obtained using the Runge‐Kutta method of the fourth order. The density of the gas is assumed to be constant. The total energy of the shock wave is non‐constant and varies with time. The effects of change in values of non‐idealness parameter, gravitational parameter, shock Mach number, radiation parameter, and adiabatic exponent of the gas on shock strength and flow variables are worked out in detail. It is investigated that the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. A comparison is also made between the solutions in the cases of the gravitating and the non‐gravitating media. It is manifested that the gravitational parameter and the radiation parameter have in general opposite behaviour on the flow variables and the shock strength.     

Solitons via Lie-Bäcklund transformation for 5D low-energy string theory

We apply a non-linear matrix transformation of Lie-Bäcklund type on a seed soliton configuration in order to obtain a new solitonic solution in the framework of the 5D low-energy effective field theory of the bosonic string. The seed solution represents a stationary axisymmetric two-soliton configuration previously constructed through the inverse scattering method and consists of a massless gravitational field coupled to a non-trivial chargeless dilaton and to an axion field endowed with charge. We apply a fully parameterized non-linear matrix transformation of Ehlers type on this massless solution and get a massive rotating axisymmetric gravitational soliton coupled to charged axion and dilaton fields. We discuss on some physical properties of both the initial and the generated solitons and fully clarify the physical effect of the non-linear normalized Ehlers transformation on the seed solution.     

The generalized uncertainty principle and the entropy of the Schwarzschild-anti-de Sitter black hole with a global monopole due to spin fields

Using the corrected state density in accordance with the generalized uncertainty principle, we investigate the quantum entropy of the Schwarzschild-anti-de Sitter black hole with a global monopole arising from fields with arbitrary spin s ≤ 2. We show that the quantum entropy depends not only on the black hole characteristics but also on the spin of the field and the gravity correction factor. The existence of the energy scale of symmetry breaking decreases the total entropy. Moreover, we show that the contribution of the gravitational interactions to the entropy is very important and should not be neglected.     

Stability of the vacuum non-singular black hole

The singularity of the black hole solutions obtained before in Møller’s theory are studied. It is found that although the two solutions reproduce the same associated metric the asymptotic behavior of the scalars of torsion tensor and basic vector are quite different. The stability of the associated metric of those solutions which is spherically symmetric non-singular black hole is studied using the equations of geodesic deviation. The condition for the stability is obtained. From this condition the stability of the Schwarzschild solution and di Sitter solution can be obtained.     

Hawking radiation as tunneling with back-reaction for the Kerr-anti-de Sitter black hole

Medved and Vagenas demonstrated how the Angheben-Nadalini-Vanzo-Zerbini analysis can be adapted in describing the effects of the gravitational back-reaction for the generic spherically symmetric black hole. We extend the Medved-Vagenas quantum tunneling method to the case of the stationary axisymmetric Kerr black hole in anti-de Sitter space-times. We find a correction to the Hawking radiation by considering the effects of the gravitational back-reaction and also energy conservation and angular momentum conservation.     

BTZ black hole as a solution of a higher-spin gauge theory in three-dimensional space-time

We show that the BTZ black hole is an exact solution of a higher-spin gauge theory in three-dimensional space-time. We find solutions for free massless fields in the black-hole metric using the star algebra formalism underlying the higher-spin theory. We find that some of the higher-spin symmetries remain unbroken for special values of the BTZ parameters. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 158–185, November, 2007.     

Dimensional reduction of gravity and relation between static states,cosmologies, and waves

We introduce generalized dimensional reductions of an integrable (1+1)-dimensional dilaton gravity coupled to matter down to one-dimensional static states (black holes in particular), cosmological models, and waves. An unusual feature of these reductions is that the wave solutions depend on two variables: space and time. They are obtained here both by reducing the moduli space (available because of complete integrability) and by a generalized separation of variables (also applicable to nonintegrable models and to higher-dimensional theories). Among these new wavelike solutions, we find a class of solutions for which the matter fields are finite everywhere in space-time, including infinity. These considerations clearly demonstrate that a deep connection exists between static states, cosmologies, and waves. We argue that it should also exist in realistic higher-dimensional theories. Among other things, we also briefly outline the relations existing between the low-dimensional models that we discuss here and the realistic higher-dimensional ones. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 422–452, December, 2007.     

Anisotropic Cosmology with a Dilaton Field Coupled to Ghost Dark Energy

We study a dilaton scalar field coupled to ghost dark energy in an anisotropic universe. The evolution of dark energy, which dominates the universe, can be completely described by a single dilaton scalar field. This connection allows reconstructing the kinetic energy and also the dynamics of the dilaton scalar field according to the evolution of the energy density. Using the latest observational data, we obtain bounds on the ghost dark energy models and also on generalized dark matter and dark energy. For this, we investigate how the expansion history H(z) is determined by observational quantities. We calculate the evolution of density perturbations in the linear regime for both ghost and generalized ghost dark energy and compare the results with ΛCDM models. We discuss the justification of the generalized second law of thermodynamics in a Bianchi type-I universe. The obtained model is stable for large time intervals but is unstable at small times.     

Exact front, soliton and hole solutions for a modified complex Ginzburg-Landau equation from the harmonic balance method

A novel approach of using harmonic balance (HB) method is presented to find front, soliton and hole solutions of a modified complex Ginzburg-Landau equation. Three families of exact solutions are obtained, one of which contains two parameters while the others one parameter. The HB method is an efficient technique in finding limit cycles of dynamical systems. In this paper, the method is extended to obtain homoclinic/heteroclinic orbits and then coherent structures. It provides a systematic approach as various methods may be needed to obtain these families of solutions. As limit cycles with arbitrary value of bifurcation parameter can be found through parametric continuation, this approach can be extended further to find analytic solution of complex quintic Ginzburg-Landau equation in terms of Fourier series.     

Quantum Gravitational Effects on the Boundary

Quantum gravitational effects might hold the key to some of the outstanding problems in theoretical physics. We analyze the perturbative quantum effects on the boundary of a gravitational system and the Dirichlet boundary condition imposed at the classical level. Our analysis reveals that for a black hole solution, there is a contradiction between the quantum effects and the Dirichlet boundary condition: the black hole solution of the one-particle-irreducible action no longer satisfies the Dirichlet boundary condition as would be expected without going into details. The analysis also suggests that the tension between the Dirichlet boundary condition and loop effects is connected with a certain mechanism of information storage on the boundary.