A study of almost pseudo 𝒵 symmetric spacetimes with application to f (R) gravity

Abstract

We prove that an almost pseudo [Formula: see text] symmetric spacetime with Codazzi type of [Formula: see text] tensor is perfect fluid whose velocity vector field [Formula: see text] is parallel. The energy density [Formula: see text] of such perfect fluid spacetime is constant and the state equation is obtained. Also, this spacetime is shown to be a static spacetime. Next, it is shown that such spacetime is a GRW spacetime with Einstein fiber. This kind of spacetime is investigated in [Formula: see text] theory of gravity; in this case, we find the forms of the isotropic pressure [Formula: see text] and the energy density [Formula: see text] which are constant. Further, some energy conditions are studied in this spacetime. Finally, a concrete example of almost pseudo [Formula: see text] symmetric spacetimes is considered.

Projective Collineations in Warped Product Manifolds and (PRS)n Manifolds

“…which illustrates that the space-time is Ricci simple [31,32]. Hence, we can conclude the following result:…”

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

“…The findings presented in this study hold great significance for geometers in their future research endeavors. For example, these results can be applied to various types of space-times, such as Z recurrent space-times [49], almost pseudo Z symmetric space-times [11], weakly Z symmetric space-times [66], and weakly cyclic Z symmetric space-times [47,48].…”

“…This groundbreaking theory not only promises to explain the observed accelerated expansion of the Universe without the need for dark energy but also opens the door to exploring exotic phenomena such as wormholes, black holes, and the nature of dark matter. With its mind-bending implications and potential to reshape our understanding of the universe, f (R) modified gravity theory stands as a captivating frontier in modern physics, engaging the minds of scientists and enthusiasts alike (for more details about this subject see [4][5][6][7][8][9][10][11] ). Among the many notable results achieved recently in this field, we would like to mention only a few.…”