Stability of Charged Thin-Shell Wormholes in (2+1) Dimensions

In this paper we construct charged thin-shell wormholes in (2+1)-dimensions applying the cut-and-paste technique implemented by Visser, from a BTZ black hole which was discovered by Bañados, Teitelboim and Zanelli (Phys. Rev. Lett. 69:1849, 1992), and the surface stress are determined using the Darmois-Israel formalism at the wormhole throat. We analyzed the stability of the shell considering phantom-energy or generalised Chaplygin gas equation of state for the exotic matter at the throat. We also discussed the linearized stability of charged thin-shell wormholes around the static solution.     

Phantom Wormholes in (2+1)-Dimensions

In this paper, we have constructed a (2+1)-dimensional wormhole using inhomogeneous and anisotropic distribution of phantom energy. We have determined the exact form of the equation of state of phantom energy that supports the wormhole structure. Interestingly, this equation of state is linear but variable one and is dependent only on the radial parameter of the model.     

Chiral Solitons in 1+2 Dimensions

This paper obtains the exact 1-soliton solution to the chiral nonlinear Schrödinger’s equation in 1+2 dimensions. Both constant coefficients and time-dependent coefficients are considered. The topological as well as bright soliton solutions are obtained. The soliton ansatz method is used to carry out the derivation of the soliton.     

New Charged Dilaton Solutions in 2+1 Dimensions and Solutions with Cylindrical Symmetry in 3+1 Dimensions

We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a compactification of charged solutions in 3+1 dimensions with cylindrical symmetry. These solutions contain naked singularities for certain values of the parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1 dimensions are generated treating the static charged solutions as seed metrics and performing SL(2;R) transformations.     

Properties of Solutions in 2 + 1 Dimensions

We solve the Einstein equations for the 2 + 1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for different solutions and compare them.     

Rotating Kink Spacetime in 2+1 Dimensions

A new family of solutions is presented for the (2+1)-dimensional Einstein equations with a rotating perfect fluid source. The mass density and pressure are everywhere positive. Features of the spacetime include closed timelike curves and Finkelstein-Misner metrical kinks.     

Rotating Dilaton Solutions in 2+1 Dimensions

We report a three parameter family of solutions for dilaton gravity in 2+1 dimensions with finite mass and finite angular momentum. These solutions are obtained by a compactification of vacuum solutions in 3+1 dimensions with cylindrical symmetry. One class of solutions corresponds to conical singularities and the other leads to curvature singularities.     

Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

The full spectrum of two‐dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of graphene, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in graphene. Here, only one Lorentz‐violating parameter is considered, belonging to the scalar sector. The analytical methods developed in the context of 1+1 field theories are extended to explore the effect of the Lorentz symmetry breaking in the charge carrier density of two‐dimensional materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. These findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.     

Singularity Free Stars in (2+1) Dimensions

We present some new types of non-singular model for anisotropic stars with constant Λ and variable Λ based on the Krori and Barua (KB) metric in (2+1) dimensions. The solutions obtained here satisfy all the regularity conditions and its simple analytical form helps us to study the various physical properties of the configuration.     

Folded Solitary Waves and Foldons in(2+1) Dimensions

A general type of localized excitations, folded solitary waves and foldons, is defined and studied bothanalytically and graphically. The folded solitary waves and foldons may be “folded“ in quite complicated ways andpossess quite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the realnatural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universalformula is valid for some quite universal (2 1)-dimensional physical models. The “universal“ formula is also extendedto a more general form with many more independent arbitrary functions.     

Folded Solitary Waves and Foldons in （2＋1） Dimensions

A general type of local/zed excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be “folded“ in quite complicated ways and possess qnite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the real natural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universal formul is valid for some quite universal (2 1)-dimensional physical mode/s. The “universal“ formula is also extended to a more general form with many more independent arbitrary functions.     

Projective Systems of Imprimitivity and Applications for the Galilei Group in 1+2 and 1+3 Dimensions

The study of the projective unitary irreducible representations of the Galilei group (in 1+3 and 1+2 dimensions) is usually done using firstly some group extensions techniques (in this way one is reduced to the study of true unitary representations) and then Mackey induction procedure. In this paper we reobtain these results using a different approach based on the notion of projective systems of imprimitivity due also to Mackey. This extension of the usual Mackey procedure is presented rather extensively and illustrated by detailed computations concerning the classification of the projective unitary irreducible representations.     

Quasinormal Modes of Charged Dilaton Black Holes in 2 + 1 Dimensions

We have studied the scalar perturbation of static charged dilaton black holes in 2 + 1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2 + 1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.     

On the Extension of Stringlike Localised Sectors in 2+1 Dimensions

In the framework of algebraic quantum field theory, we study the category \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) of stringlike localised representations of a net of observables \({\mathcal{O} \mapsto \mathfrak{A}(\mathcal{O})}\) in three dimensions. It is shown that compactly localised (DHR) representations give rise to a non-trivial centre of \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) with respect to the braiding. This implies that \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) cannot be modular when non-trivial DHR sectors exist. Modular tensor categories, however, are important for topological quantum computing. For this reason, we discuss a method to remove this obstruction to modularity.Indeed, the obstruction can be removed by passing from the observable net \({\mathfrak{A}(\mathcal{O})}\) to the Doplicher-Roberts field net \({\mathfrak{F}(\mathcal{O})}\). It is then shown that sectors of \({\mathfrak{A}}\) can be extended to sectors of the field net that commute with the action of the corresponding symmetry group. Moreover, all such sectors are extensions of sectors of \({\mathfrak{A}}\). Finally, the category \({\Delta_{{\rm BF}}^{\mathfrak{F}}}\) of sectors of \({\mathfrak{F}}\) is studied by investigating the relation with the categorical crossed product of \({\Delta_{{\rm BF}}^{\mathfrak{A}}}\) by the subcategory of DHR representations. Under appropriate conditions, this completely determines the category \({\Delta_{{\rm BF}}^{\mathfrak{F}}}\).     

Novel Rotating Hairy Black Hole in （2 ＋ 1） Dimensions

We present some novel rotating hairy black hole metric in （2 ＋ 1） dimensions, which is an exact solution to the field equations of the Einstein-scalar-AdS theory with a non-minimal coupling. The scalar potential is determined by the metric ansatz and consistency of the field equations and cannot be prescribed arbitrarily. In the simplified, critical ease, the scalar potential contains two independent constant parameters, which are respectively related to the mass and angular momentum of the black hole in a particular way. As long as the angular momentum does not vanish, the metric can have zero, one or two horizons. The case with no horizon is physically uninteresting because of the curvature singularity lying at the origin. We identify the necessary conditions for at least one horizon to be present in the solution, which imposes some bound on the mass-angular momentum ratio. For some particular choice of pararneters our solution degenerates into some previously known black hole solutions.     

A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions

Abstract

The Singular Manifold Method (SMM) is applied to an equation in 2 + 1 dimensions [13] that can be considered as a generalization of the sine-Gordon equation. SMM is useful to prove that the equation has two Painlevé branches and, therefore, it can be considered as the modified version of an equation with just one branch, that is the AKNS equation in 2 + 1 dimensions. The solutions of the former split as linear superposition of two solutions of the second, related by a B¨acklund-gauge transformation. Solutions of both equations are obtained by means of an algorithmic procedure derived from these transformations.     

Supersymmetric Integrable Systems in (2 + 1) Dimensions and Their Backlund Transformation

Nonlinear integrable systems in (2 + 1)dimensions which are supersymmetric are generated in twodifferent ways. In one approach the homogeneous spacesof super-Lie algebra are used, and in the other we use a different technique of extending thedimension of the system. The two sets of equations turnout to be different. The methodologies ofDarbux–Backlund transformation and gaugetransformation are used to generate the Backlund transformations ofthese equations. An important result of our analysis isthe existence of purely fermionic nonlinear systems in(2 + 1) dimensions.