Symmetries and charges of general relativity at null boundaries
Symmetries and charges of general relativity at null boundaries
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DOI：
10.1007/jhep11(2018)125
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发表时间：
2018-07
影响因子：
5.4
通讯作者：
V. Chandrasekaran;E. Flanagan;Kartik Prabhu
中科院分区：
文献类型：
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作者：
V. Chandrasekaran;E. Flanagan;Kartik Prabhu
我们用协变相空间形式研究了零边界上的广义相对论。我们定义了一个协变相空间，并通过考虑保持该相空间的保边微分同胚，计算了零边界上的对称代数。这个代数是两个球面上的微分同胚的半直和，它是一个非交换的超平移代数，它与零无穷远的超平移有一些相似之处。利用Wald和Zoupas发展的一般公式，我们导出了该代数在零点表面横截面上的定域电荷以及相应的通量。我们的分析是协变的，适用于一般的非平稳零曲面。我们还导出了产生事件视界对称性的整体电荷，并且证明了这些对称性与线性化的微分同胚遵循相同的代数，没有任何中心扩张。我们的结果表明，超平移不仅在零点无穷远，而且在所有零点边界，包括动态事件视界，都扮演着重要的角色。它们应该有助于进一步研究黑洞时空中的视界对称性和守恒定律是否像霍金、佩里和斯特罗明格所建议的那样，在信息丢失问题中发挥作用。
We study general relativity at a null boundary using the covariant phase space formalism. We define a covariant phase space and compute the algebra of symmetries at the null boundary by considering the boundary-preserving diffeomorphisms that preserve this phase space. This algebra is the semi-direct sum of diffeomorphisms on the two sphere and a nonabelian algebra of supertranslations that has some similarities to supertranslations at null infinity. By using the general prescription developed by Wald and Zoupas, we derive the localized charges of this algebra at cross sections of the null surface as well as the associated fluxes. Our analysis is covariant and applies to general non-stationary null surfaces. We also derive the global charges that generate the symmetries for event horizons, and show that these obey the same algebra as the linearized diffeomorphisms, without any central extension. Our results show that supertranslations play an important role not just at null infinity but at all null boundaries, including non-stationary event horizons. They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.