Proposed Theorems on a Lorentzian K¨ ahler Space-time Manifold Admitting Bochner Curvature Tensor
Proposed Theorems on a Lorentzian K¨ ahler Space-time Manifold
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Keywords:Differential equations, Partial differential equations, Cosmology, Nonlinear equations, Theory of Relativity,, Lorentzian K¨ahler space-time manifolds, Bochner curvature tensor
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
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