This work studies the Hawking energy in a cosmological context. The past lightcone of a point in spacetime is the natural geometric structure closely linked to cosmological observations. By slicing the past lightcone into a 1-parameter family of spacelike 2-surfaces, the evolution of the Hawking energy down the lightcone is studied. Strong gravitational fields may generate lightcone self-intersections and wave front singularities. We show that in the presence of swallow-tail type singularities, the Hawking energy and its variation along the null generators of the lightcone remains well-defined and subsequently discuss its positivity and monotonicity.

中文翻译：

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宇宙学中过去光锥上的霍金能量

这项工作在宇宙学背景下研究霍金能量。时空中一个点的过去光锥是与宇宙观测密切相关的自然几何结构。通过将过去的光锥切割成一个 1 参数的类空间 2 表面族，研究了沿着光锥的霍金能量的演化。强引力场可能会产生光锥自相交和波前奇点。我们表明，在燕尾型奇点存在的情况下，霍金能量及其沿光锥零发生器的变化仍然是明确定义的，随后讨论了它的正性和单调性。