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arXiv 2304.06752hep-thgr-qc
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Gibbons-Hawking-York边界项与广义引力几何三位一体

Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity

Johanna Erdmenger, Bastian Heß, Ioannis Matthaiakakis, René Meyer

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Accepted for publication in Physical Review D, 9 + 4 pages, v2: Additional boundary terms included to Sec. IV, citations added
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AI总结：

本文在度量-仿射引力框架中研究Gibbons-Hawking-York边界项在GR、TEGR和STEGR之间的变化关系，证明边界项B为GHY项之差且TEGR与STEGR的GHY项必须为零，并将三者等价性推广到任意曲率二形式作用量，建立广义引力几何三位一体。

摘要：

广义相对论（GR）通过爱因斯坦-希尔伯特作用量以曲率描述，在动力学上等价于以时空挠率或非度量性表述的引力理论。这构成了所谓的引力几何三位一体。除GR外，与该三位一体对应的理论分别是远平行等效理论（TEGR）和对称远平行等效理论（STEGR），它们的作用量在边界项$B$之内与GR等价。我们在度量-仿射引力框架内研究GR的Gibbons-Hawking-York（GHY）边界项在向TEGR和STEGR过渡时如何变化。我们证明$B$是GR的GHY项与度量-仿射引力的GHY项之差。此外，我们证明TEGR和STEGR的GHY项必须为零，以保证变分问题的一致性。更进一步，我们的方法允许将GR、TEGR和STEGR之间的等价性从爱因斯坦-希尔伯特作用量扩展到任何由曲率二形式构成的作用量，从而建立广义引力几何三位一体。我们认为这些结果对于研究具有挠率和非度量性的理论的规范/引力对偶将特别有用。

英文摘要：

General relativity (GR) as described in terms of curvature by the Einstein-Hilbert action is dynamically equivalent to theories of gravity formulated in terms of spacetime torsion or non-metricity. This forms what is called the geometrical trinity of gravity. The theories corresponding to this trinity are, apart from GR, the teleparallel (TEGR) and symmetric teleparallel (STEGR) equivalent theories of general relativity, respectively, and their actions are equivalent to GR up to boundary terms $B$. We investigate how the Gibbons-Hawking-York (GHY) boundary term of GR changes under the transition to TEGR and STEGR within the framework of metric-affine gravity. We show that $B$ is the difference between the GHY term of GR and that of metric-affine gravity. Moreover, we show that the GHY term for both TEGR and STEGR must vanish for consistency of the variational problem. Furthermore, our approach allows to extend the equivalence between GR, TEGR and STEGR beyond the Einstein-Hilbert action to any action built out of the curvature two-form, thus establishing the generalized geometrical trinity of gravity. We argue that these results will be particularly useful in view of studying gauge/gravity duality for theories with torsion and non-metricity.

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