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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 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.