Spacelike translating solitons of mean curvature flow with forcing term in Lorentzian product spaces

In this paper we study translating solitons with a forcing term immersed in a Lorentzian product space R-1 xP(n). Under suitable curvature constraints on the curvatures of the Riemannian base P-n we deduce an Omori-Yau maximum principle, and as applications we get a nonexistence result. Besides, we also prove that any entire spacelike downward translating graph that never intersects null infinity is mean convex. Furthermore, under suitable assumption on the base P-n, we prove a boundedness of the second fundamental form of such translating solitons.