arXiv subjects

Bülent Ünal

Publications and source records attributed to Bülent Ünal.

6 recordsLinked to original sources

arXiv2026

Bochner Flatness and Soliton Dynamics in Lorentzian Kähler Spacetime Geometry

We study Riemann solitons and $η$-hyperbolic Ricci solitons on Bochner-flat Lorentzian Kähler spacetime manifolds. Under the Einstein field equations with cosmological constant and perfect fluid assumptions, explicit formulas for the soliton parameter are derived, yielding criteria for shrinking, steady, and expanding behaviors. Several physically relevant models, including dark fluid, stiff matter, dust, and radiation, are analyzed. We show that Bochner-flat Lorentzian Kähler spacetimes are Einstein and investigate the resulting geometric and dynamical consequences. In the context of generalized Robertson--Walker spacetimes, we obtain constraints on the warping function and classify soliton solutions. Global properties such as geodesic completeness, singularity formation, and stability are also examined.

math.DG↗

arXiv2022

Gradient $ρ$-Einstein Solitons and Applications

In this paper, we mainly study gradient $ρ$-Einstein solitons on doubly warped product manifolds. More explicitly, we obtain necessary and sufficient conditions for a doubly warped product manifold to be a gradient $ρ$-Einstein soliton. We also apply our main result to warped product spacetime models such as generalized Robertson-Walker and standard static spacetimes as well as 3-dimensional Walker manifolds. We finally establish that there is no 3-dimensional esentially conformally symmetric gradient $ρ$-Einstein soliton.

math.DG↗

arXiv2022

Pseudo-Projective Tensor on Sequential Warped Products

The main objective of this paper is to study pseudo-projective tensor on sequential warped products and then to obtain necessary and sufficient conditions for a sequential warped product to be pseudo-projectively flat. Moreover, we also provide characterization of pseudo-projectively flat sequential generalized Robertson-Walker and pseudo-projectively flat sequential standard static spacetimes.S

math.DG↗

arXiv2021

Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime

The aim of the present paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson-Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson-Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein's field equations without cosmological constant is vacuum. Finally, we construct a non-trivial example of pseudosymmetric spacetime.

gr-qc↗

arXiv2020

Generalized Quasi Yamabe Gradient Solitons and Applications

The purpose of this article is to study generalized quasi Yamabe gradient solitons on warped product manifolds. First, we obtain some necessary and sufficient conditions for the existence of generalized quasi Yamabe gradient solitons equipped with the warped product structure. Then we study three important applications in the Lorentzian and the neutral settings for the particular class, called as gradient Yamabe soliton: We proved the existence of the non-trivial gradient Yamabe soliton on generalized Robertson-Walker spacetimes, standard static spacetimes and Walker manifolds.

math.DG↗

arXiv2019

Sequential Warped Products: Curvature and Killing Vector Fields

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker spacetimes and sequential standard static spacetimes.

math.DG↗