This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [7, 26, 27] and define the quasi-local energy as differences of surface Hamiltonians. The ground state for the gravitational energy is taken to be a reference configuration in the de Sitter (dS) or Anti‑de Sitter (AdS) spacetime. This defines the quasi-local energy with respect to the reference spacetime and generalizes our previous definition with respect to the Minkowski spacetime. Through an optimal isometric embedding into the reference spacetime, the Killing fields of the reference spacetime are transplanted back to the surface in the physical spacetime to complete the definitions of quasi-local conserved quantities. We also compute how the corresponding total conserved quantities evolve under the Einstein equation with a cosmological constant.

中文翻译：

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关于de Sitter / anti-de Sitter参考的准局部能量

本文考虑了具有宇宙学常数的参考时空的准局部守恒量。我们遵循作者[7，26，27]中开发的方法，并将准局部能量定义为表面哈密顿量的差异。在de Sitter（dS）或Anti-de Sitter（AdS）时空中，重力能的基态被视为参考配置。这定义了相对于参考时空的准局部能量，并概括了我们先前关于Minkowski时空的定义。通过将最佳等轴测图嵌入到参考时空中，可以将参考时空的Killing场在物理时空中移植回地面，以完成对准局部守恒量的定义。