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    ?Anti-commutable? local pre-Leibniz algebroids and admissible connections
    (Elsevier, 2023) Dereli, Tekin; Dogan, Keremcan
    The concept of algebroid is convenient as a basis for constructions of geometrical frameworks. For example, metric-affine and generalized geometries can be written on Lie and Courant algebroids, respectively. Furthermore, string theories might make use of many other algebroids such as metric algebroids, higher Courant algebroids, or conformal Courant algebroids. Working on the possibly most general algebroid structure, which generalizes many of the algebroids used in the literature, is fruitful as it creates a chance to study all of them at once. Local pre-Leibniz algebroids are such general ones in which metric-connection geometries are possible to construct. On the other hand, the existence of the 'locality operator', which is present for the left-Leibniz rule for the bracket, necessitates the modification of torsion and curvature operators in order to achieve tensorial quantities. In this paper, this modification of torsion and curvature is explained from the point of view that the modification is applied to the bracket instead. This leads one to consider 'anti-commutable' local pre-Leibniz algebroids which satisfy an anti-commutativity-like property defined with respect to a choice of an equivalence class of connections. These 'admissible' connections are claimed to be the necessary ones while working on a geometry of algebroids. This claim is due to the fact that one can prove many desirable properties and relations if one uses only admissible connections. For instance, for admissible connections, we prove the first and second Bianchi identities, Cartan structure equations, Cartan magic formula, the construction of Levi-Civita connections, the decomposition of connection in terms of torsion and non-metricity. These all are possible because the modified bracket becomes anti-symmetric for an admissible connection so that one can apply the machinery of almost-or pre-Lie algebroids. We investigate various algebroid structures from the literature and show that they admit admissible connections which are metric-compatible in some generalized sense. Moreover, we prove that local pre-Leibniz algebroids that are not anti-commutable cannot be equipped with a torsion-free, and in particular Levi-Civita, connection. (c) 2023 Elsevier B.V. All rights reserved.
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    Dark range of ? in brans-dicke gravity
    (IOP Science, 2022) Dereli, Tekin; Şenikoğlu, Yorgo
    The variational field equations of Brans-Dicke scalar-tensor theory of gravitation that is coupled to a mass-varying sterile neutrino field are presented in Riemannian and non-Riemannian setting in the language of exterior differential forms over four-dimensional spacetime. In a gravitational plane wave geometry in Rosen coordinates, with the scalar field set equal to a constant, the field equations admit ghost neutrino solutions. These correspond to Majorana spinor configurations for which the total neutrino stress-energy-momentum tensor vanishes. We show here that in the absence of a sterile neutrino in the gravitational wave geometry, there are scalar field configurations for which the total scalar field stress-energy-momentum tensor vanishes for negative values of the Brans-Dicke parameter ?3/2 < ? < 0.
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    General teleparallel metrical geometries
    (World Scientific Publ Co Pte Ltd, 2023) Adak, Muzaffer; Dereli, Tekin; Koivisto, Tomi S.; Pala, Caglar
    In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead described by torsion and nonmetricity. These so called general teleparallel geometries may also have applications in material physics, such as the study of crystal defects. In this work, we explore the general teleparallel geometry in the language of differential forms. We discuss the special cases of metric and symmetric teleparallelisms, clarify the relations between formulations with different gauge fixings and without gauge fixing, and develop a method of recasting Riemannian into teleparallel geometries. As illustrations of the method, exact solutions are presented for the generic quadratic theory in 2, 3 and 4 dimensions.
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    Neutrino fields in a sandwich gravitational wave background
    (Iop Publishing Ltd, 2022) Dereli, Tekin; Gürtuğ, Özay; Halilsoy, Mustafa; Senikoğlu, Yorgo
    Sandwich gravitational waves are given globally in terms of step functions at the boundaries. Linearized Einstein-Weyl equations are solved exactly in this background in Rosen coordinates. Depending on the geometry and composition of the sandwich wave, the neutrino's energy-momentum redistributes itself. At the test field level, since the background will not change, the neutrino's energy density in particular will show variations between positive and negative extrema when crossing the sandwich wave. This may reveal facts about the weakly interacting neutrinos in cosmology.
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    A note on the pp-wave solution of minimal massive 3D gravity coupled with Maxwell-Chern-Simons theory
    (Iop Publishing Ltd, 2022) Cebeci, Hakan; Dereli, Tekin; Sentorun, Secil
    In this work, we examine a family of pp-wave solutions of minimal massive 3D gravity minimally coupled with the Maxwell-Chern-Simons theory. An elaborate investigation of the field equations shows that the theory admits pp-wave solutions provided that there exist an anti-self duality relation between the electric and the magnetic components of the Maxwell two-form field. By employing Noether-Wald formalism, we also construct Noether charges of the theory within exterior algebra formalism.
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    Simple supergravity pp-waves
    (General Relativity and Gravitation, 2022) Dereli, Tekin; Şenikoğlu, Yorgo
    Non-gauge generated exact solutions of simple supergravity field equations that describe pp-waves in Rosen coordinates are presented in the language of complex quaternion valued exterior differential forms.
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    Variational field equations of a Majorana neutrino coupled to Einstein's theory of general relativity
    (Tubitak Scientific & Technological Research Council Turkey, 2022) Dereli, Tekin; Senikoğlu, Yorgo
    A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The Lagrange multiplier 2-forms we use turn out to be precisely the Belinfante-Rosenfeld 2-forms that are needed to symmetrize the canonical energy-momentum tensor of the Majorana spinor.
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    Weyl neutrinos in plane symmetric spacetimes
    (General Relativity and Gravitation, 2023) Dereli, Tekin; Şenikoğlu, Yorgo
    We investigate complex quaternion-valued exterior differential forms over 4-dimensional Lorentzian spacetimes and explore Weyl spinor fields as minimal left ideals within the complex quaternion algebra. The variational derivation of the coupled Einstein–Weyl equations from an action is presented, and the resulting field equations for both first and second order variations are derived and simplified. Exact plane symmetric solutions of the Einstein–Weyl equations are discussed, and two families of exact solutions describing left-moving and right-moving neutrino plane waves are provided. The study highlights the significance of adjusting a quartic self-coupling of the Weyl spinor in the action to ensure the equivalence of the field equations.