On almost Kenmotsu manifolds admitting nearly vacuum static equations with applications

In this article, we study certain characteristics of nearly vacuum static equations on almost Kenmotsu manifolds. It is established that an η-Einstein almost Kenmotsu manifold allowing nearly vacuum static equations is of constant scalar curvature and either the solution is trivial or, the manifold reduces to an Einstein manifold. Next, nearly vacuum static equations on (κ,μ)-almost Kenmotsu manifolds and generalized (κ,μ)'-nullity distribution are considered and we obtain several interesting results. Moreover, we illustrate that if a 3-dimensional Kenmotsu manifold allows nearly vacuum static equations, then the manifold is locally isometric to the hyperbolic space Η3(-1). After that, we investigate a spacetime satisfying nearly vacuum static equations endowed with a parallel vector field and obtain that such a spacetime is a perfect fluid spacetime as well as a generalized Robertson-Walker spacetime. Finally, we construct a non trivial example of almost Kenmotsu manifold with (κ,μ)'-nullity distribution.