In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, $(m,\rho )$-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime. We also characterize the m-quasi Einstein standard static spacetimes admitting concurrent or parallel vector fields and get several physical properties of such spacetimes. At last, we construct non-trivial examples of m-quasi Einstein spacetimes verifying our results.

在本文中，首先，我们刻画了满足某些 Ricci-Hessian 类方程的标准静态时空，例如广义拟爱因斯坦流形、m-拟爱因斯坦流形、$(米,\rho )$-准爱因斯坦流形和梯度 Ricci 孤子。然后，我们得到了标准静态时空上某些向量场存在的充要条件。我们还刻画了允许并发或平行矢量场的m -准爱因斯坦标准静态时空，并获得了这种时空的几个物理特性。最后，我们构建了m-准爱因斯坦时空的非平凡例子来验证我们的结果。