Characterizations of perfect fluid spacetimes obeying f(R)-gravity equipped with different gradient solitons

초록

The prime object of this paper is to study the perfect fluid spacetimes obeying f(R)-gravity, when eta-Ricci solitons, gradient eta-Ricci solitons, gradient Einstein solitons and gradient m-quasi Einstein solitons are its metrics. At first, the existence of the eta-Ricci solitons is proved by a non-trivial example. We establish conditions for which the eta-Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying f(R)-gravity, when the potential vector field of eta-Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient eta-Ricci solitons, gradient Einstein solitons and gradient m-quasi Einstein solitons in f(R)-gravity, respectively. As a result, we establish some significant theorems about dark matter era.

키워드