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 [25,26,7] 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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相对于 de Sitter/anti-de Sitter 参考的准局部能量

本文考虑了相对于具有宇宙学常数的参考时空的准局域守恒量。我们遵循作者在 [25,26,7] 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。重力能量的基态被视为德西特 (dS) 或反德西特 (AdS) 时空中的参考配置。这定义了关于参考时空的准局域能量，并概括了我们之前关于 Minkowski 时空的定义。通过最优等距嵌入参考时空，将参考时空的Killing场移植回物理时空的表面，完成准局域守恒量的定义。