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Öğe A unified approach to variational derivatives of modified gravitational actions(IOP PUBLISHING LTD, 2011) Baykal, Ahmet; Delice, OZgurOur main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modified gravitational Lagrangian densities in spacetime dimensions n >= 3. We study the well-known gravitational actions such as those involving the Gauss-Bonnet and Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic generalizations similar to generic f(R) theories and the algebraic generalization of sixth order gravitational Lagrangians. We put forth a new model involving the gravitational Chern-Simons term and also give three-dimensional new massive gravity equations in a new form in terms of the Cotton 2-form.Öğe An alternative derivation of the minimal massive 3D gravity(IOP PUBLISHING LTD, 2015) Baykal, AhmetBy using the algebra of exterior forms and the first order formalism with constraints, an alternative derivation of the field equations for the minimal massive 3D gravity model is presented.Öğe Cylindrically symmetric Brans-Dicke-Maxwell solutions(SPRINGER/PLENUM PUBLISHERS, 2009) Baykal, Ahmet; Delice, OezgurWe investigate cylindrically symmetric vacuum solutions with both null and non-null electromagnetic fields in the framework of the Brans-Dicke theory and compare these solutions with some of the well-known solutions of general relativity for special values of the parameters of the resulting field functions. We see that, unlike general relativity where the gravitational force of an infinite and charged line mass acting on a test particle is always repulsive, it can be attractive or repulsive for Brans-Dicke theory depending on the values of the parameters as well as the radial distance from the symmetry axis.Öğe Cylindrically symmetric vacuum solutions in higher dimensional Brans-Dicke theory(AMER INST PHYSICS, 2010) Baykal, Ahmet; Ciftci, Dilek K.; Delice, OezguerHigher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the Brans-Dicke theory are presented. We show that for a negative cosmological constant and for specific values of the parameters, a particular subclass of these solutions includes higher dimensional topological black hole-type solutions with a flat horizon topology. We briefly extend our discussion to stationary vacuum and Lambda-vacuum solutions. (C) 2010 American Institute of Physics. [doi:10.1063/1.3459939]Öğe Energy definition for quadratic curvature gravities(AMER PHYSICAL SOC, 2012) Baykal, AhmetA conserved current for generic quadratic curvature gravitational models is defined, and it is shown that, at the linearized level, it corresponds to the Deser-Tekin charges. An explicit expression for the charge for new massive gravity in three dimensions is given. Some implications of the linearized equations are discussed.Öğe Generalized Sparling-Thirring form in the Brans-Dicke theory(Springer, 2015) Baykal, Ahmet; Delice, OzgurThe definition of the Sparling-Thirring form is extended to Brans-Dicke theory. By writing the Brans-Dicke field equations in a formally Maxwell-like form, a superpotential and a corresponding pseudo-energy-momentum form are defined. The general energy expression provided by the superpotential in the Jordan frame is discussed in relation to the corresponding expression in the Einstein frame. In order to substantiate its formal definition, the generalized Sparling-Thirring form is used to calculate the energy for the spherically symmetric vacuum solution in Brans-Dicke theory.Öğe Gravitational wave solutions of quadratic curvature gravity using a null coframe formulation(AMER PHYSICAL SOC, 2014) Baykal, AhmetQuadratic curvature gravity equations are projected to a complex null coframe by using the algebra of exterior forms and expressed in terms of the spinor quantities defined originally by Newman and Penrose. As an application, a new family of impulsive gravitational wave solutions propagating in various Petrov type D backgrounds is introduced.Öğe Laguerre polynomials by a harmonic oscillator(IOP PUBLISHING LTD, 2014) Baykal, Melek; Baykal, AhmetThe study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.Öğe Linearized gravity in terms of differential forms(Springer Heidelberg, 2017) Baykal, Ahmet; Dereli, TekinA technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior algebra of differential forms.Öğe Modified Einstein-Gauss-Bonnet gravity: Riemann-Cartan and pseudo-Riemannian cases(SPRINGER HEIDELBERG, 2016) Ozer, Hatice; Baykal, Ahmet; Delice, OzgurA modified Einstein-Gauss-Bonnet gravity in four dimensions where the quadratic Gauss-Bonnet term is coupled to a scalar field is considered. The field equations of the model are obtained by variational methods by making use of the constrained first-order formalism covering both pseudo-Riemannian and non-Riemannian cases. In the pseudo-Riemannian case, the Lagrange multiplier forms, which impose the vanishing torsion constraint, are eliminated in favor of the remaining fields and the resulting metric field equations are expressed in terms of the double dual curvature 2-form. In the non-Riemannian case with torsion, the field equations are expressed in terms of the pseudo-Riemannian quantities by a perturbative scheme valid for a weak coupling constant. It is shown that, for both cases, the model admits a maximally symmetric de Sitter solution with non-trivial scalar field. Minimal coupling of a Dirac spinor to the Gauss-Bonnet modified gravity is also discussed briefly.Öğe Multi-scalar-tensor equivalents for modified gravitational actions(AMER PHYSICAL SOC, 2013) Baykal, Ahmet; Delice, OzgurA general scheme of constructing scalar-tensor equivalents to modified gravitational actions are studied using the algebra of exterior differential forms and the first order formalism that allows an independent connection and coframe. By introducing appropriate constraints on the connection, pseudo-Riemannian cases as well as non-Riemannian cases are discussed for various gravitational models. The issue of the dynamical degree of freedom for the resulting scalar fields is discussed at the level of the field equations. Explicit scalar-tensor equivalents for gravitational models based on f(R) models, the quadratic curvature Lagrangians and the models involving the gradients of the scalar curvature are presented. In particular, explicit scalar-tensor equivalence for gravitational Lagrangians popular in some cosmological models are constructed.Öğe Nonminimally coupled Einstein-Maxwell model in a non-Riemann spacetime with torsion(AMER PHYSICAL SOC, 2015) Baykal, Ahmet; Dereli, TekinA system of field equations for an Einstein-Maxwell model with RF2-type nonminimal coupling in a non-Riemannian space-time with a nonvanishing torsion is derived and the resulting field equations are expressed in terms of the Riemannian quantities based on a metric with a Lorentzian signature. The torsion is generated by the gradients of the electromagnetic field invariants. An electromagnetic constitutive tensor is introduced in the formulation of the field equations.Öğe pp-waves in modified gravity(SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2016) Baykal, AhmetThe family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a self-contained and coherent manner by using a variant of the null coframe formulation of Newman and Penrose and the exterior algebra of differential forms on pseudo-Riemannian manifolds.Öğe Preface by the guest editors(TUBITAK, 2016) Gürtu?, Özay; Turgut, Teoman; Baykal, Ahmet[No abstract available]Öğe Quadratic curvature gravity with second order trace and massive gravity models in three dimensions(SPRINGER/PLENUM PUBLISHERS, 2012) Baykal, AhmetThe quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In n > 4 dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions under which the latter is "square root" of the former are presented.Öğe The pseudoharmonic oscillator energy spectrum(Iop Publishing Ltd, 2022) Baykal, Melek; Baykal, AhmetThe solution to the one dimensional Schrodinger equation for the potential of type x (2) + alpha x (-2), for positive values of the constant alpha is discussed using an operator method by factorizing the Hamiltonian.Öğe Variational derivatives of gravitational actions(SPRINGER HEIDELBERG, 2013) Baykal, AhmetA method of calculation for the constrained variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first-order formalism with constraints. The proposed method calculation is then used to derive the metric field equations for a generic f (R) model.
