(m,ρ)-quasi-Einstein solitons on 3-dimensional trans-Sasakian manifolds and its applications in spacetimes

This paper characterizes [Formula: see text]-quasi-Einstein solitons on [Formula: see text]-dimensional trans-Sasakian manifolds. It has been shown that a closed [Formula: see text]-quasi-Einstein soliton on a [Formula: see text]-dimensional trans-Sasakian manifold is either cosymplectic or Einstein under certain restrictions. Moreover, we investigate [Formula: see text]-quasi-Einstein solitons with certain potential vector fields on [Formula: see text]-dimensional trans-Sasakian manifolds. As an application of this soliton, we also analyze super quasi-Einstein spacetimes whose metrics are associated with [Formula: see text]-quasi-Einstein solitons.