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arXiv 1802.00399gr-qchep-th
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非定域无鬼无奇引力的经典性质

Classical properties of non-local, ghost- and singularity-free gravity

Luca Buoninfante, Alexey S. Koshelev, Gaetano Lambiase, Anupam Mazumdar

摘要:

本文给出了引力无穷导数鬼理论和无奇性理论在静态极限下的所有线性化曲率张量。我们发现,在非定域区域,在紫外区(离源很近),里奇张量和里奇标量并没有消失,这意味着我们不再有真空解,这是由于非定域引力相互作用的存在引起的源的涂抹。这也表明,与爱因斯坦的引力不同,黎曼张量不是无迹的,它与外尔张量不一致。其次,这些曲率在短距离处被正则化,使得它们是无奇异性的,特别是对于Kretschmann不变量也是如此。与其他的不同,外尔张量在短距离处消失,这意味着时空度规在非定域区域,即紫外区域,变得共形平坦。因此,非局部区域可以用具有非负常曲率的共形平坦流形来近似。我们简要地讨论了在非线性制度的解决方案,并认为,$1/r$度规势不能解决非局域性是很重要的紫外区。

英文摘要:

In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with the Weyl tensor. Secondly, these curvatures are regularized at short distances such that they are singularity-free, in particular the same happens for the Kretschmann invariant. Unlike the others, the Weyl tensor vanishes at short distances, implying that the spacetime metric becomes conformally flat in the region of non-locality, in the ultraviolet. As a consequence, the non-local region can be approximated by a conformally flat manifold with non-negative constant curvatures. We briefly discuss the solution in the non-linear regime, and argue that $1/r$ metric potential cannot be the solution where non-locality is important in the ultraviolet regime.

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