  In this paper, we study entire translating solutions $u(x)$ to a mean
curvature flow equation in Minkowski space. We show that if $\Sigma=\{(x,
u(x))| x\in\mathbb{R}^n\}$ is a strictly spacelike hypersurface, then $\Sigma$
reduces to a strictly convex rank k soliton in $\mathbb{R}^{k, 1}$ (after
splitting off trivial factors) whose "blowdown" converges to a multiple
$\lambda\in(0, 1)$ of a positively homogeneous degree one convex function in
$\mathbb{R}^k$. We also show that there is nonuniqueness as the rotationally
symmetric solution may be perturbed to a solution by an arbitrary smooth order
one perturbation.
