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.
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BibTeX
@misc{ramasamya2026bochner,
title = {{Bochner Flatness and Soliton Dynamics in Lorentzian Kähler Spacetime Geometry}},
author = {Karthika Ramasamya and Lavanya Kumara and Soumendu Roy and Bülent Ünal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.25464},
eprint = {2606.25464},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25464},
}
RIS
TY - UNPB
TI - Bochner Flatness and Soliton Dynamics in Lorentzian Kähler Spacetime Geometry
AU - Karthika Ramasamya
AU - Lavanya Kumara
AU - Soumendu Roy
AU - Bülent Ünal
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2606.25464
UR - https://arxiv.org/abs/2606.25464
AB - 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.
ER -