Characterizations of Generalized Quasi-Einstein Space-Times

The current article’s goal is to characterize generalized quasi-Einstein space-times. Two nontrivial examples have been provided to demonstrate the existence of such a space-time. It is shown that a generalized quasi-Einstein space-time represents a Ricci recurrent space-time, and the associated vectors are parallel. Moreover, we prove that a Ricci-symmetric generalized quasi-Einstein space-time is static. Next, we establish that a Ricci-semi-symmetric generalized quasi-Einstein space-time is a perfect fluid space-time under some restriction on the associated scalars. Moreover, we illustrate that a generalized quasi-Einstein twisted space-time becomes a perfect fluid space-time under certain condition, and also find the conditions under which this space-time represents a radiation era, a dust matter era and a dark matter era of the universe. Also, we see that if the space-time has a Riemann compatible (also, Weyl compatible) vector, and the space-time is purely electric. Finally, we acquire under what condition a generalized quasi-Einstein twisted space-time becomes a generalized Robertson–Walker space-time.