In all \(n(\ge 3)\)-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking–Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that, if back-reaction is taken into account to give a self-consistent solution, ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms. As a consequence, a static Planck-mass relic is possible as a final state of an evaporating black hole only if the semiclassical total energy-momentum tensor is of type I.

在所有\(n(\ge 3)\)维引力理论中，其拉格朗日函数是黎曼张量和度量的函数，我们表明，除非物质场的总能量-动量张量是 I 型，否则不存在静态解。霍金-埃利斯分类。换句话说，在具有 II、III 或 IV 型能量-动量张量的时空区域中不存在超曲面正交时态杀伤向量。这断言，如果考虑反向反应来给出自洽解，那么即使具有更高曲率的校正项，具有半经典 IV 型物质场的超密集区域也不能是静态的。因此，只有当半经典总能量-动量张量是 I 型时，静态普朗克质量遗迹才有可能作为蒸发黑洞的最终状态。