On m-quasi-Einstein spacetimes
In this paper, we have studied [Formula: see text]-quasi-Einstein spacetimes. Some basic results of such spacetimes are derived. Perfect and viscous fluid [Formula: see text]-quasi-Einstein spacetimes are also studied and the expressions of pressure, cosmological constant and energy density are obtained. We have proved that if the generator [Formula: see text] of an [Formula: see text]-quasi-Einstein spacetime is a Killing vector field, then the spacetime is either conformally flat or of Petrov-type [Formula: see text]. It is also shown that if the function [Formula: see text] of an [Formula: see text]-quasi-Einstein spacetime satisfying Einstein’s equation is harmonic and the matter distribution is perfect fluid, then Segre’ characteristics of the Ricci tensor is [(1,1), 1]. Finally, an example is constructed for the proper existence of such a spacetime.