Michail D. Todorov

ELECTRICALLY CHARGED EINSTEIN–BORN–INFELD BLACK HOLES WITH MASSIVE DILATON

We numerically construct static and spherically symmetric electrically charged black hole solutions in Einstein–Born–Infeld gravity with massive dilaton. The numerical solutions show that the dilaton potential allows many more black hole causal structures than the massless dilaton. We find that depending on the black hole mass and charge and the dilaton mass, the black holes can have either one, two, or three horizons. The extremal solutions are also found. As an interesting peculiarity we note that there are extremal black holes with an inner horizon and with triply degenerated horizon.

PHASES OF 4D SCALAR–TENSOR BLACK HOLES COUPLED TO BORN–INFELD NONLINEAR ELECTRODYNAMICS

Recent results show that when nonlinear electrodynamics is considered, the no-scalar-hair theorems in the scalar–tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented.1,2 What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to nonlinear electrodynamics in a special class of scalar–tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar–tensor theories considered, the black holes have a single, non-degenerate horizon, i.e. their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.

SCALAR–TENSOR BLACK HOLES COUPLED TO EULER–HEISENBERG NONLINEAR ELECTRODYNAMICS

The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of nonlinear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler–Heisenberg type nonlinear electrodynamics in scalar–tensor theories of gravity with massless scalar field are found. In comparison to the corresponding solution in General Relativity the presented solution has a simpler causal structure the reason for which is the presence of the scalar field. The present class of black holes has a single, nondegenerate horizon, i.e. its causal structure resembles that of the Schwarzschild black hole.

Charged anti–de Sitter scalar-tensor black holes and their thermodynamic phase structure

In the present paper we numerically construct new charged anti-de Sitter black holes coupled to nonlinear Born-Infeld electrodynamics within a certain class of scalar-tensor theories. The properties of the solutions are investigated both numerically and analytically. We also study the thermodynamics of the black holes in the canonical ensemble. For large values of the Born-Infeld parameter and for a certain interval of the charge values we find the existence of a first-order phase transition between small and very large black holes. An unexpected result is that for a certain small charge subinterval two phase transitions have been observed, one of zeroth and one of first order. It is important to note that such phase transitions are also observed for pure Einstein-Born-Infeld-AdS black holes.

Mathematical Modeling of Boson-Fermion Stars in the Generalized Scalar-Tensor Theories of Gravity

A model of static boson–fermion stars with spherical symmetry based on the scalar–tensor theory of gravity with a massive dilaton field is investigated numerically. Since the radius of the star is a priori an unknown quantity, the corresponding boundary value problem is treated as a nonlinear spectral problem with a free internal boundary. The continuous analogue of Newton method is used to solve this problem. Information about basic geometric functions and the functions describing the matter fields which build the star is obtained. From a physical point of view the main result is that the structure and properties of the star in the presence of a massive dilaton field depend essentially on both its fermionic and bosonic comp-onents.

Boson stars in massive dilatonic gravity

We study equilibrium configurations of boson stars in the framework of a class scalar-tensor theories of gravity with massive gravitational scalar (dilaton). In particular we investigate the influence of the mass of the dilaton on the boson star structure. We find that the masses of the boson stars in presence of dilaton are close to those in general relativity and they are sensitive to the ratio of the boson mass to the dilaton mass within a typical few percent. It turns out also that the boson star structure is mainly sensitive to the mass term of the dilaton potential rather to the exact form of the potential.

Adiabatic interactions of Manakov solitons—Effects of cross-modulation

Abstract We investigate the asymptotic behavior of the Manakov soliton trains perturbed by cross-modulation in the adiabatic approximation. The multisoliton interactions in the adiabatic approximation are modeled by a generalized Complex Toda chain (GCTC). The cross-modulation requires special treating for the evolution of the polarization vectors of the solitons. The numerical predictions of the Manakov system are compared with the perturbed GCTC. For certain set of initial parameters GCTC describes very well the long-time evolution of the Manakov soliton trains.

Self-compression of high-intensity femtosecond laser pulses in a low-dispersion regime

Self-compression of high-intensity femtosecond laser pulses and more than an order of magnitude increase of the peak intensity are found in a medium of positive group velocity dispersion based on the lowest order optical processes in the (3+1)-dimensional nonlinear Schrodinger equation. A physical mechanism of the pulse compression and intensity gain in a low-dispersion regime is proposed for the first time. A method of high-intensity femtosecond pulse formation can be developed on this basis.

A numerical algorithm for modelling of boson-fermion stars in dilatonic gravity

We investigate numerically class of models of the static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem. The first of the parameters is the unknown internal boundary (the radius of the fermionic part of the star) Rs, and the second one represents the frequency Ω of the time oscillations of the bosonic field.To solve this problem, the whole space [0,∞) is splitted in two domains: internal [0,Rs] (inside the star) and external [Rs, ∞) (outside the star). In each domain the physical model leads to two nonlinear boundary value problems in respect of metric functions, the functions describing the fermionic and bosonic matter, and the dilaton field. These boundary value problems have different dimensions inside and outside the star, respectively. The solutions in these regions are obtained separately and matched using the necessary algebraic continuity conditions including Rs and Ω. The continuous analogue of Newton method for solving both the nonlinear differential and algebraic problems is used.The proposed method essentially differs from that one explained in our paper (J. Comput. Phys. 166 (2) (2001) 253) and ensures certain advantages. In this way, we obtain the behavior of the basic geometric quantities and functions describing a dilaton field and matter fields, which build the star.

Asymptotic behavior of Manakov solitons

We consider the asymptotic behavior of the soliton solutions of Manakovs system perturbed by external potentials. It has already been established that its multisoliton interactions in the adiabatic approximation can be modeled by the complex Toda chain (CTC). The fact that the CTC is a completely integrable system, enables us to determine the asymptotic behavior of the multisoliton trains. In the present study we accent on the 3-soliton initial configurations perturbed by sech-like external potentials and compare the numerical predictions of the Manakov system and the perturbed CTC in different regimes. The results of conducted analysis show that the perturbed CTC can reliably predict the long-time evolution of the Manakov system. The asymptotics of soliton solutions of the perturbed Manakov system is considered.Three-soliton chains perturbed by sech-like external potentials are studied.The Manakov system and the perturbed complex Toda chain are compared.Perturbed complex Toda chain predicts the long-time evolution of the Manakov system.