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Yayın The charged Zipoy–Voorhees metric with astrophysical applications(The European Physical Journal C, 2022) Gürtuğ, Özay; Halilsoy, Mustafa; Mangut, Mert; Gürtuğ, ÖzayStarting from an integral of the interaction region of colliding Einstein–Maxwell waves and by applying a coordinate transformation, we obtain the charged version of the static Zipoy–Voorhees (Z V) metric valid for all values of the distortion parameter ? . In Schwarzschild coordinates, we investigate the effect of the charge in the newly found spacetime, stress the analogy with Reissner–Nordstrom metric and discuss some of its features. It is shown that from the expression of Weyl curvature, directional singularities become manifest. For astrophysical importance, we find lensing of null geodesics from the Gauss–Bonnet theorem in such non-spherically charged objects. To prepare the ground for our null, circular geodesics we consider the angular equation linearized about the symmetry plane ? = ?/2. This, in turn, suggests the distortion parameter (the Z V parameter) must be in the interval 1/2Yayın Effect of power-law Maxwell field to the gravitational lensing(APS Physics, 2019) Gürtuğ, Özay; Mangut, Mert; Gürtuğ, ÖzayIn this paper, we extend the gravitational bending of light studies in Kottler metrics to comprise nonlinear electrodynamics within the framework of Einstein - power - Maxwell theory. We show that the closest approach distance and the gravitational bending of light are affected from the presence of charge for particular values of the power parameter k, which is defined by means of energy conditions. It is shown that the bending angle of light is stronger in the case of a strong electric field, which is the case for k = 1.2.Yayın Gravitational lensing in a model of nonlinear electrodynamics: the case for electrically and magnetically charged compact objects(Wiley Online Library, 2020) Gürtuğ, Özay; Mangut, Mert; Gürtuğ, ÖzayThis paper aims to investigate the astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov (Ann. Phys. Berlin 2017, 529, 170073). Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coincide with the linear case and it becomes hard to identify the effect of nonlinearity. However, the calculation of the redshift has shown that while the increase in the electric field leads to a decrease in the gravitational redshift,the presence of the strong magnetic field contributes to the gravitational redshift in an increasing manner.Yayın Gravitational lensing in rotating and twisting universes(Elsevier, 2021) Gürtuğ, Özay; Mangut, Mert; Halilsoy, Mustafa; Gürtuğ, ÖzayGravitational lensing caused by the gravitational field of massive objects has been studied and acknowledged for a long period of time. In this paper, however, we propose a different mechanism where the bending of light stems from the non-linear interaction of gravitational, electromagnetic and axion waves that creates the high curvature zone in the space-time fabric. The striking distinction in the present study is that in contrast to the convex lensing in the gravitational field of a massive object, hyperbolic nature of the high curvature zone of the background space-time may give rise to concave lensing. Expectedly detection of this kind of lensing becomes possible through satellite detectors.Yayın Kuantum tekillik analizinin matematiksel temelleri: Horava-Lifshitz teorisindeki uygulamaları(Maltepe Üniversitesi, Fen Bilimleri Enstitüsü, 2018-07) Mangut, Mert; Gürtuğ, ÖzayBu tezde, kuantum tekillik analizinin matematiksel dayanak noktaları ve bu analizin matematiği ele alınarak Horava – Lifshitz teorisindeki uygulaması yapılmıştır. İlk olarak, gerekli matematiksel altyapı olan; topolojik uzaylar, metrik uzaylar, vektör uzayları, normlu uzaylar, iç çarpım uzayları ve Hilbert uzayı gözden geçirilerek temel teoremler ispatlanarak, gerekli temel tanımlar yapılmıştır. İkinci olarak ise, uzay – zaman tekillikleri tanımlanarak kuantum tekillik analizinin dayandığı matematiksel temel ve kriterler verilerek, operatörlerin özde (essentially) self – adjointliğinin belirlenmesi için gerekli teoremlerin ispatları yapılmış ve bu analizin iki temel metodu olan özde (essentially) self – adjointliğin temel kriteri ve Weyl limit noktası – limit çemberi kriteri, ispatları ile verilmiştir. Daha sonra uygulama, önemli bir alternatif gravitasyon teorisi olan Horava – Lifshitz teorisinde yer alan Kehagias – Sfetsos küresel simetrik karadelik çözümünün çıplak tekillik şartı çerçevesinde yapılarak, Klein-Gordon ve Dirac denklemlerinden elde edilen diferansiyel operatörlerin uzaysal kısmının özde (essentially) self – adjointliği bu iki farklı metot ile incelenmiştir. Yapılan analizde klasik olarak tekil olan uzay – zaman yapısının kuantum mekaniksel olarak tekil olmadığı gösterilmiştir.Yayın Probing naked singularities in the charged and uncharged ? - metrics with quantum wave packets(Springer/Plenum Publishers, 2023) Gurtug, Ozay; Halilsoy, Mustafa; Mangut, MertThe non-trivial naked singularities that possess directional behavior in the charged and uncharged Zipoy-Voorhees (ZV) spacetimes, known as ? - metrics are investigated within the context of quantum mechanics. Classically singular spacetime is understood as a geodesic incompleteness with respect to a particle probe, while quantum singularity is understood as a non-unique evolution of test quantum wave packets. In this study, quantum wave packets obeying Klein-Gordon equation are used to probe timelike naked singularities. It is shown by rigorous mathematical calculations that the outermost singularity developed in the charged and uncharged ZV spacetime on the equatorial plane is quantum mechanically singular for all values of the deformation parameter ?. However, directional singularities that develop on the symmetry axis is shown to be healed partially for specific range of the parameter ?, if the analysis is restricted purposely to only specific mode (s-wave mode). Allowing arbitrary modes, classical directional singularities remains quantum singular.Yayın Quantum probe of Ho?rava-lifshitz gravity(Cornell University, 2018) Gürtuğ, Özay; Mangut, Mert; Gürtuğ, ÖzayParticle probe analysis of the Kehagias - Sfetsos black hole spacetime of Ho?rava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The timelike naked singularity that develops when ?M 2 < 1 /2, is probed with quantum fields obeying KleinGordon and Chandrasekhar-Dirac equations. Quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint and thus, the naked singularity in the Kehagias - Sfetsos spacetime become quantum mechanically non - singular.Yayın Quantum probe of time-like naked singularities for electrically and magnetically charged black holes in a model of nonlinear electrodynamics(World Scientific Connecting Great Minds, 2020) Mangut, Mert; Gürtuğ, Özay; Gürtuğ, ÖzayThe time-like naked singularities of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated within the framework of quantum mechanics. In view of quantum mechanics, the space-time is quantum regular provided that the time evolution of the test quantum wave packet uniquely propagates on an underlying background. Rigorous calculations have shown that when the singularity is probed with specific quantum wave/particle modes, the quantum wave operator turns out to be essentially self-adjoint. Thus, the time evolution of the quantum wave/particle is determined uniquely. In the case of electrically charged black hole background, the unique evolution is restricted to s-wave only. For the two different magnetically charged black hole backgrounds, the time evolution is restricted to different modes for each case.
