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T. Dereli

Publications and source records attributed to T. Dereli.

At least 19 recordsLinked to original sources
arXiv2016

New Improved Massive Gravity and Three Dimensional Spacetimes of Constant Curvature and Constant Torsion

We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find variational field equations both in the presence and absence of torsion. We then show that spaces of constant negative curvature (i.e. the anti de-Sitter space $AdS_3$) and constant torsion provide exact solutions.

gr-qc↗
arXiv2011

Born-Infeld Axion-Dilaton Electrodynamics and Electromagnetic Confinement

A generalization of Born-Infeld non-linear vacuum electrodynamics involving axion and dilaton fields is constructed with couplings dictated by electromagnetic duality and SL(2,R) symmetries in the weak field limit. Besides the Newtonian gravitational constant the model contains a single fundamental coupling parameter b0. In the absence of axion and dilaton interactions it reduces, in the limit as b0 tends to infinity, to Maxwell's linear vacuum theory while for finite b0 it reduces to the original Born-Infeld model. The spherically symmetric static sector of the theory is explored in a background Minkowski spacetime where numerical evidence suggests the existence of axion-dilaton bound states possessing confined electric flux.

hep-th↗
arXiv2011

Non-minimally Coupled Gravitational and Electromagnetic Fields: pp-Wave Solutions

We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.

gr-qc↗
arXiv2010

Einstein-Cartan-Dirac Theory in (1+2)-Dimensions

Einstein-Cartan theory is formulated in (1+2)-dimensions using the algebra of exterior differential forms. A Dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. The space-time torsion is found to be given algebraically in terms of the Dirac field. Circularly symmetric, exact solutions that collapse to AdS_3 geometry in the absence of a Dirac spinor are found.

gr-qc↗
arXiv2010

Charged relativistic fluids and non-linear electrodynamics

The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.

math-ph↗
arXiv2009

Canonical transformations in three-dimensional phase space

Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

math-ph↗
arXiv2009

Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism

A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one attempts to construct the three basic transformations in star-product form, while gauge and point transformations are immediate in star-exponential form, interchange has no correspondent, but it is possible in an ordinary exponential form. As an alternative approach, it is shown that all three basic transformations can be constructed in the ordinary exponential form and that in some cases this approach provides more useful tools than the star-exponential form in finding the generating function for given canonical transformation or vice versa. It is also shown that transforms of c-number phase space functions under linear-nonlinear canonical transformations and intertwining method can be treated within this argument.

math-ph↗
arXiv2008

The Quadratic Symmetric Teleparallel Gravity in Two-Dimensions

A 2D symmetric teleparallel gravity model is given by a generic 4-parameter action that is quadratic in the non-metricity tensor. Variational field equations are derived. A class of conformally flat solutions is given. We also discuss static and cosmological solutions.

hep-th↗
arXiv2007

Coherence lifetimes of excitations in an atomic condensate due to the thin spectrum

We study the quantum coherence properties of a finite sized atomic condensate using a toy-model and the thin spectrum model formalism. The decoherence time for a condensate in the ground state, nominally taken as a variational symmetry breaking state, is investigated for both zero and finite temperatures. We also consider the lifetimes for Bogoliubov quasi-particle excitations, and contrast them to the observability window determined by the ground state coherence time. The lifetimes are shown to exhibit a general characteristic dependence on the temperature, determined by the thin spectrum accompanying the spontaneous symmetry breaking ground state.

quant-ph↗
arXiv2007

Exact Solutions in Five-Dimensional Axi-dilaton Gravity with Euler-Poincare Term

We examine the effective field equations that are obtained from the axi-dilaton gravity action with a second order Euler-Poincare term and a cosmological constant in all higher dimensions. We solve these equations for five-dimensional spacetimes possessing homogeneity and isotropy in their three-dimensional subspaces. For a number of interesting special cases we show that the solutions fall into two main classes: The first class consists of time-dependent solutions with spherical or hyperboloidal symmetry which require certain fine-tuning relations between the coupling constants of the model and the cosmological constant. Solutions in the second class are locally static and prove the validity of Birkhoff's staticity theorem in the axi-dilaton gravity. We also give a special class of static solutions, among them the well-known black hole solutions in which the usual electric charge is superseded by an axion charge.

gr-qc↗
arXiv2007

Linear Connections on Light-like Manifolds

It is well-known that a torsion-free linear connection on a light-like manifold $(M,g)$ compatible with the degenerate metric $g$ exists if and only if $Rad(TM)$ is a Killing distribution. In case of existence, there is an infinitude of connections with none distinguished. We propose a method to single out connections with the help of a special set of 1-forms by the condition that the 1-forms become parallel with respect to this connection. Such sets of 1-forms could be regarded as an additional structure imposed upon the light-like manifold. We consider also connections with torsion and with non-metricity on light-like manifolds.

math.DG↗
arXiv2006

Degenerate Spin Structures and the Levy-Leblond Equation

Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton-Cartan 4-manifold by the aid of degenerate spin group. Levy-Leblond equation is constructed with the lifted connection.

math-ph↗
arXiv2006

New Perspectives On the Relevance of Gravitation for the Covariant Description of Electromagnetically Polarizable Media

Electromagnetic properties of a simple polarisable medium may be parameterised in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial (accelerating) frames and in the presence of weak but variable gravitational fields. After establishing some geometric notation, discussion is given to basic concepts of stress, energy and momentum in the vacuum where the useful notion of a drive form is introduced in order to associate the conservation of currents involving the flux of energy, momentum and angular momentum with spacetime isometries. The definition of the stress-energy-momentum tensor is discussed with particular reference to its symmetry based on its role as a source of relativistic gravitation. General constitutive properties of material continua are formulated in terms of spacetime tensors including those that describe magneto-electric phenomena in moving media. This leads to a formulation of a self-adjoint constitutive tensor describing, in general, inhomogeneous, anisotropic, magneto-electric bulk matter in arbitrary motion. The question of an invariant characterisation of intrinsically magneto-electric media is explored. An action principle is established to generate the phenomenological Maxwell system and the use of variational derivatives to calculate stress-energy-momentum tensors is discussed in some detail. The relation of this result to tensors proposed by Abraham and others is discussed in the concluding section where the relevance of the whole approach to experiments on matter in non-inertial environments with variable gravitational and electromagnetic fields is stressed.

math-ph↗
arXiv2006

The Covariant Description of Electromagnetically Polarizable Media

The form of the phenomenological stress-energy-momentum tensor for the electromagnetic field in a class of inhomogeneous, anisotropic magneto-electric media is calculated from first principles, leading to a coherent understanding of the phenomenological stresses and energy-momentum exchanges induced by electromagnetic interactions with such matter in terms of a fully relativistic covariant variational framework.

math-ph↗
arXiv2005

Gravitational field equations in a braneworld with Euler-Poincare term

We present the effective gravitational field equations in a 3-brane world with Euler-Poincare term and a cosmological constant in the bulk spacetime. The similar equations on a 3-brane with $\mathbb{Z}_2$ symmetry embedded in a five dimensional bulk spacetime were obtained earlier by Maeda and Torii using the Gauss-Coddazzi projective approach in the framework of the Gaussian normal coordinates. We recover these equations on the brane in terms of differential forms and using a more general coordinate setting in the spirit of Arnowitt, Deser and Misner (ADM). The latter allows for acceleration of the normals to the brane surface through the lapse function and the shift vector. We show that the gravitational effects of the bulk space are transmitted to the brane through the projected ``electric'' 1-form field constructed from the conformal Weyl curvature 2-form of the bulk space. We also derive the evolution equations into the bulk space for the electric 1-form field, as well as for the ``magnetic'' 2-form field part of the bulk Weyl curvature 2-form. As expected, unlike on-brane equations, the evolution equations involve terms determined by the nonvanishing acceleration of the normals in the ADM-type slicing of spacetime.

hep-th↗