Solitons and black holes

Abstract. We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point of view, the mechanism allows one to select the speed of a SG soliton just by tuning elastic couplings constants and kinematical parameters. From a fundamental, field-theoretical point of view we show that the characterizing features of relativistic SG solitons (existence of conserved topological charges and stability) may be still preserved even if the Lorentz symmetry is broken and a soliton of a given speed is selected.

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“…We are only interested in the symmetries relevant for the solitonic solutions, namely in the symmetries of the reduced Lagrangian (25).…”

Section: Discrete Symmetries and Topological Classificationmentioning

confidence: 99%

A symmetry breaking mechanism for selecting the speed of relativistic solitons

Cadoni

Лео

Gaeta

2007

J. Phys. A: Math. Theor.

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“…Frames of similar type have appeared [7,8,9] in 2-dimensional dilaton gravity. The connection and the curvature of the analogous commutative moving frame arẽ…”

Section: Fuzzy Doughnutmentioning

confidence: 93%

A dynamical 2-dimensional fuzzy space

Burić¹,

Madore²

2005

Physics Letters B

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“…In two recent papers [9] Gegenberg and Kunstatter investigated the relationship between black holes of JT dilation gravity and solutions of the sine-Gordon field theory. Their constructions were generalized by Cadoni [6] to soliton solutions of 2D dilaton gravity models which describes spacetimes being of non constant curvature.…”

Section: B Locally Anisotropic Soliton Black Hole and Disk/cylindermentioning

confidence: 99%

“…The matrix g ij (x i ) will be defined by some Gegenberg-Kunstatter-Cadoni 2D soliton-black hole solutions [9,6], their conformal transforms, or by the factor f (x i ) from (1.4) which could be related with solitons for h ab . We emphasize that the resulting 4D (pseudo) Riemannian metrics, with generic local anisotropy (in brief, la-metrics) will be found to solve the Einstein equations with energy-momentum tensor.…”

Section: B Locally Anisotropic Soliton Black Hole and Disk/cylindermentioning

confidence: 99%

Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity

Vacaru

2001

J. High Energy Phys.

245

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A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with associated nonlinear connections, the structure of gravity field equations is substantially simplified. It is shown that there are 4D solutions of Einstein equations which are constructed as nonlinear superpositions of soliton solutions of 2D (pseudo) Euclidean sine-Gordon equations (or of Lorentzian black holes in Jackiw-Teitelboim dilaton gravity). The Belinski-Zakharov-Meison solitons for vacuum gravitational field equations are generalized to various cases of two and three coordinate dependencies, local anisotropy and matter sources. The general framework of this study is based on investigation of anholonomic soliton-dilaton black hole structures in general relativity. We prove that there are possible static and dynamical black hole, black torus and disk/cylinder like solutions (of non-vacuum gravitational field equations) with horizons being parametrized by hypersurface equations of rotation ellipsoid, torus, cylinder and another type configurations. Solutions describing locally anisotropic variants of the Schwarzschild-Kerr (black hole), Weyl (cylindrical symmetry) and Nogebauer-Meinel (disk solution) with anisotropic variable masses, distributions of matter and interaction constants are shown to be contained in Einstein's gravity. It is demonstrated in which manner locally anisotropic multi-soliton-dilaton-black hole type solutions can be generated. 98.80.Cq, 04.50.+h, 98.80.Hw, 02.90.+p, 04.70.Bw, 11.10Kk E-preprint: gr-qc/0005xxx

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Solitons and black holes

Cited by 26 publications

References 10 publications

A symmetry breaking mechanism for selecting the speed of relativistic solitons

A symmetry breaking mechanism for selecting the speed of relativistic solitons

A dynamical 2-dimensional fuzzy space

Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity

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