We investigate whether supertranslation symmetry may appear in a scenario that involves black holes in AdS space. The framework we consider is massive 3D gravity, which admits a rich black hole phase space, including stationary AdS black holes with softly decaying hair. We consider a set of asymptotic conditions that permits such decaying near the boundary, and which, in addition to the local conformal symmetry, is preserved by an extra local current. The corresponding algebra of diffeomorphisms consists of two copies of Virasoro algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then reorient the analysis to the near horizon region, where infinite-dimensional symmetries also appear. The supertranslation symmetry at the horizon yields an infinite set of non-trivial charges, which we explicitly compute. The zero-mode of these charges correctly reproduces the black hole entropy. In contrast to Einstein gravity, in the higher-derivative theory subleading terms in the near horizon expansion contribute to the near horizon charges. Such terms happen to capture the higher-curvature corrections to the Bekenstein area law.

中文翻译：

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AdS 中的地平线对称性和毛茸茸的黑洞

我们研究了超平移对称性是否可能出现在涉及 AdS 空间中的黑洞的场景中。我们考虑的框架是巨大的 3D 引力，它允许一个丰富的黑洞相空间，包括带有软衰减头发的静止 AdS 黑洞。我们考虑一组渐近条件，允许在边界附近进行这种衰减，并且除了局部共形对称之外，还通过额外的局部电流来保持。微分同胚的相应代数由 Virasoro 代数的两个副本组成，它们是具有无限维阿贝尔理想的半直和。然后我们将分析重新定向到近地平线区域，在那里也出现了无限维对称性。地平线上的超平移对称性产生了一组无限的非平凡电荷，我们明确地计算了这些电荷。这些电荷的零模式正确地再现了黑洞熵。与爱因斯坦引力相反，在高导数理论中，近地平线膨胀中的子主导项对近地平线电荷有贡献。这些术语恰好捕捉到对 Bekenstein 面积定律的更高曲率修正。