Perturbations of general relativity to all orders and the general nth order terms

被引：5
作者：
Cho, Kyoungho [1 ]
Kim, Kwangeon [2 ]
Lee, Kanghoon [1 ,3 ]
机构：
[1] Postech, Asia Pacific Ctr Theoret Phys, Pohang 37673, South Korea
[2] Yonsei Univ, Dept Phys, Seoul 03722, South Korea
[3] Postech, Dept Phys, Pohang 37673, South Korea
来源：
JOURNAL OF HIGH ENERGY PHYSICS | 2023年 / 2023卷 / 03期
关键词：
Classical Theories of Gravity; Scattering Amplitudes; AMPLITUDES;
D O I：
10.1007/JHEP03(2023)112
中图分类号：
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号：
摘要：
We derive all-order expressions for perturbations of the Einstein-Hilbert action and the Einstein equation with the general n-th order terms. To this end, we employ Cheung and Remmen's perturbation conventions both in tensor density and the usual metric tensor formalisms, including the Einstein-dilaton theory. Remarkably, we find minimal building blocks that generate the entire perturbations for each of our formulations. We show that the number of terms of perturbations grows linearly as the order of perturbations increases. We regard our results as the reference and discuss how to derive perturbations in other conventions from the reference. As a consistency check, we compute graviton scattering amplitudes using the perturbiner method based on the perturbative Einstein equation. Finally we discuss how to generalise the results to curved backgrounds and incorporate additional matter.
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页数：38
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