发表机构
Institute of Mathematics of the Czech Academy of Sciences; Charles University（捷克科学院数学研究所; 查理大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究广义相对论teleparallel等价形式中引力作用的正则化，通过自旋联络作为抵消项消除歧义，并证明正则化方案的唯一性。
AI 中文摘要
我们研究了广义相对论的teleparallel等价形式中的引力作用，其中自旋联络通过一个表面项对作用做出贡献，并且当选择适当时，通过有效扮演抵消项的角色来正则化作用。我们以Schwarzschild时空为例，解决了该过程中的几个明显歧义。我们表明，体作用与准局域作用之间的明显差异源于与时空奇点相关的贡献，并且准局域作用与广义相对论中获得的标准结果一致。我们进一步阐明了tetrad选择在确定相应自旋联络中的作用，表明适当的对角框架和正则框架给出相同的欧几里得作用，而只有适当的对角框架在Wheeler-DeWitt片上重现预期的洛伦兹作用。最后，我们确立了正则化方案的唯一性，并表明施加适当的挠率张量衰减行为可消除剩余歧义并唯一确定欧几里得作用。
英文摘要
We study the gravitational action in the teleparallel equivalent of general relativity, where the spin connection contributes to the action through a surface term and, when chosen appropriately, regularizes the action by effectively playing the role of a counterterm. We resolve several apparent ambiguities in this procedure using the Schwarzschild spacetime as an example. We show that the apparent discrepancy between bulk and quasilocal actions originates from contributions associated with spacetime singularities, and that the quasilocal action agrees with the standard results obtained in general relativity. We further clarify the role of the tetrad choice in determining the corresponding spin connection, showing that the proper diagonal and canonical frames give the same Euclidean action, while only the proper diagonal frame reproduces the expected Lorentzian action on the Wheeler--DeWitt patch. Finally, we establish the uniqueness of the regularization scheme and show that imposing an appropriate fall-off behavior of the torsion tensor removes the remaining ambiguity and fixes the Euclidean action uniquely.
Comments24 pages, no figure
