Proposed Theorems on a Lorentzian K¨ ahler Space-time Manifold Admitting Bochner Curvature Tensor: Proposed Theorems on a Lorentzian K¨ ahler Space-time Manifold

B. B. Chaturvedi; Prabhawati Bhagat; Mohammad Nazrul Islam Khan; Tazeen Rana; Ratnesh Kumar Mishra

Authors

B. B. Chaturvedi Guru Ghasidas Vishwavidyalaya (A Central University)
Prabhawati Bhagat Guru Ghasidas Vishwavidyalaya (A Central University)
Mohammad Nazrul Islam Khan Qassim University
Tazeen Rana Qassim University
Ratnesh Kumar Mishra Central university of jharkhand Ranchi

Keywords:

Differential equations, Partial differential equations, Cosmology, Nonlinear equations, Theory of Relativity,, Lorentzian K¨ahler space-time manifolds, Bochner curvature tensor

Abstract

The objective of this paper is to investigate the Lorentzian K¨ahler space-time manifold that is Bochner flat. We have demonstrated that a Lorentzian K¨ahler space-time manifold with Bochner flatness is also an Einstein manifold. Furthermore, we have established that the energy-momentum tensor is covariantly constant when the manifold satisfies the Einstein field equation with a cosmological constant. Additionally, we have determined that the energy-momentum tensor of a perfect fluid Lorentzian K¨ahler space-time manifold exhibits hybrid characteristics. In the final section, we analyse the behavior of a dust fluid Lorentzian K¨ ahler space-time manifold where the Bochner
curvature vanishes.

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Proposed Theorems on a Lorentzian K¨ ahler Space-time Manifold Admitting Bochner Curvature Tensor