Bochner Flatness and Soliton Dynamics in Lorentzian Kähler Spacetime Geometry

Abstract

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.