Solitons of the spacelike mean curvature flow in generalized Robertson-Walker spacetimes

Our purpose in this paper is to study solitons of the spacelike mean curvature flow in a generalized Robertson-Walker (GRW) spacetime -I x(f )M(n). Under suitable constraints on the warping function f and on the curvatures of the Riemannian fiber M-n, we apply suitable maximum princi-ples in order to obtain nonexistence and uniqueness results concerning these solitons. Applications to standard models of GRW spacetimes, namely, the Einstein-de Sitter spacetime, steady state type spacetimes, de Sitter and anti -de Sitter spaces, are given. Furthermore, we establish new Calabi-Bernstein type results related to entire spacelike mean curvature flow graphs constructed over the Riemannian fiber of the ambient spacetime.