We study the existence/nonexistence and multiplicity of spacelike graphs for the following mean curvature equation in a standard static spacetime
$ \begin{eqnarray} \text{div} \left(\frac{a\nabla u}{\sqrt{1-a^2\vert \nabla u\vert^2}}\right)+\frac{g(\nabla u, \nabla a)}{\sqrt{1-a^2\vert \nabla u\vert^2}} = \lambda NH \end{eqnarray} $
with $ 0 $-Dirichlet boundary condition on the unit ball. According to the behavior of $ H $ near $ 0 $, we obtain the global structure of one-sign radial spacelike graphs for this problem. Moreover, we also obtain the existence and multiplicity of entire spacelike graphs.
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Bifurcation diagrams of Theorem 1.1