论文标题
沿轻酮切割的较高尺寸的准能量的小球极限
The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts
论文作者
论文摘要
准能量的问题主要在四个维度上进行了广泛的研究。在这里，我们报告有关时空维度$ n \ geq 4 $中的准能量的结果。在适当的假设下将三个不同的准能定义概括为更高维度之后，我们评估了它们的小球体沿灯酮切割的小球限制，从而缩小了朝灯顶点。真空的结果以Weyl张量的电磁分解为方便地表示。我们发现，存在物质的限制会产生预期的压力张量，但是真空限制通常与Bel-Robinson超级货币$ Q $ q $ in dimensions $ n> 4 $成正比。该结果无视Bel-Robinson超级美食在更高维度中表征重力能量的作用，尽管它具有唯一的概括。令人惊讶的是，霍金能量和棕色能量完全同意各个维度的小球体的限制。但是，新的真空限制$ \ MATHCAL {Q} $，由于其非阳性，因此无法解释为引力能量。此外，我们还提供了更高尺寸的Kijowski-epp-liu-yau型能量的小球体限制，我们再次看到$ \ Mathcal {q} $代替$ q $。我们的工作扩展了对小球限制的早期研究[1、2、3、4]，并且还补充了[5]。
The problem of quasilocal energy has been extensively studied mainly in four dimensions. Here we report results regarding the quasilocal energy in spacetime dimension $n\geq 4$. After generalising three distinct quasilocal energy definitions to higher dimensions under appropriate assumptions, we evaluate their small sphere limits along lightcone cuts shrinking towards the lightcone vertex. The results in vacuum are conveniently represented in terms of the electromagnetic decompositions of the Weyl tensor. We find that the limits at presence of matter yield the stress tensor as expected, but the vacuum limits are in general not proportional to the Bel-Robinson superenergy $Q$ in dimensions $n>4$. The result defies the role of the Bel-Robinson superenergy as characterising the gravitational energy in higher dimensions, albeit the fact that it uniquely generalises. Surprisingly, the Hawking energy and the Brown-York energy exactly agree upon the small sphere limits across all dimensions. The new vacuum limit $\mathcal{Q}$, however, cannot be interpreted as a gravitational energy because of its non-positivity. Furthermore, we also give the small sphere limits of the Kijowski-Epp-Liu-Yau type energy in higher dimensions, and again we see $\mathcal{Q}$ in place of $Q$. Our work extends earlier investigations of the small sphere limits [1, 2, 3, 4], and also complements [5].
