标题： 曲率约束临界面上霍金准局部能量的刚性和正性 显示英文标题

标题： Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces

摘要： 任何广义相对论中的准局部能量的关键测试是它应为非负的并满足刚性性质；如果它为零，所包含的区域是平直的。 我们证明，在其自然面积约束临界表面上计算的霍金能量，此后称为“霍金面”，在主导能量条件下满足这两个性质。 在时间对称的情况下，霍金面与面积约束的威姆斯表面重合，我们将正性和刚性扩展到包括电荷、非零宇宙常数和高维情况。 在完全动态（非时间对称）的情况下，我们在这种一般情况下建立了霍金能量的第一个非负性和刚性定理。 这些结果确认了霍金能量符合基本物理原理，并解决了几个长期存在的模糊性和批评。 显示英文摘要

摘要： A key test for any quasi-local energy in general relativity is that it be nonnegative and satisfy a rigidity property; if it vanishes, the region enclosed is flat. We show that the Hawking energy, when evaluated on its natural area-constrained critical surfaces, henceforth called "Hawking surfaces", satisfies both properties under the dominant energy condition. In the time-symmetric case, where Hawking surfaces coincide with area-constrained Willmore surfaces, we extend positivity and rigidity to include electric charge, a nonzero cosmological constant, and higher dimensions. In the fully dynamical (non-time-symmetric) case, we establish the first nonnegativity and rigidity theorems for the Hawking energy in this general setting. These results confirm the Hawking energy consistency with basic physical principles and address several longstanding ambiguities and criticisms.