arXiv subjects
Publications and source records attributed to Ahmet Baykal.
The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by the Riemann curvature tensor. The linearized metric field equations are formulated in terms of perturbation 1-form fields.
The Lanczos potential for the Weyl tensor is derived from a quadratic curvature Lagrangian by making use of the exterior algebra of forms and the variational principles with constraints.
We linearize vacuum Einstein field equations with a cosmological constant around a curved background to elaborate on the reconstruction of the Abbott-Deser charges and incorporate a spin connection into the definition using the algebra of differential forms on a given curved background spacetime.
Impulsive, non-diverging, Petrov-Segre type N gravitational wave solutions to a general massive three-dimensional gravity in the de Sitter, anti-de Sitter and flat Minkowski backgrounds are constructed in a unified manner by using the exterior algebra of differential forms.
The 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.
A 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.
A 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 nontrivial scalar field. Minimal coupling of a Dirac spinor to the Gauss-Bonnet modified gravity is also discussed briefly.
A system of field equations for an Einstein-Maxwell model with $RF^2$-type nonminimal coupling in a non-Riemannian space-time with a non-vanishing 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.
By 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.
The definition of the Sparling-Thirring form is extended to the 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 the Brans-Dicke theory.
Quadratic 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 type D backgrounds is introduced.
A 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 ST equivalence for gravitational lagrangians popular in some cosmological models are constructed.
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric field equations for a generic $f(R)$ model.
A 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.
The 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.
Our 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 $n\geqslant 3$. We study 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.
Higher 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 include higher dimensional topological black hole-type solutions with a flat horizon topology. We briefly extend our discussion to stationary vacuum and $Λ-$vacuum solutions.
The factorization method of Infeld and Hull is applied to the radial Schrödinger equation for $d$-dimensional isotropic harmonic oscillator and various ladder operators are defined. The radial energy eigenstates are expressed in terms of the generalized Laguerre polynomials and their properties are shown to follow from the expressions involving the ladder operators. In the same way as the harmonic oscillator we also obtain the bound energy eigenstates of the Morse oscillator.