Perturbations of general relativity to all orders and the general n th order terms
Abstract 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 Eins...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2023)112 |
| _version_ | 1797795833830178816 |
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| author | Kyoungho Cho Kwangeon Kim Kanghoon Lee |
| author_facet | Kyoungho Cho Kwangeon Kim Kanghoon Lee |
| author_sort | Kyoungho Cho |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-03-13T03:25:00Z |
| format | Article |
| id | doaj.art-303e25d7c1c8443b9ff09d503868a38a |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-13T03:25:00Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-303e25d7c1c8443b9ff09d503868a38a2023-06-25T11:07:12ZengSpringerOpenJournal of High Energy Physics1029-84792023-03-012023313810.1007/JHEP03(2023)112Perturbations of general relativity to all orders and the general n th order termsKyoungho Cho0Kwangeon Kim1Kanghoon Lee2Asia Pacific Center for Theoretical Physics, PostechDepartment of Physics, Yonsei UniversityAsia Pacific Center for Theoretical Physics, PostechAbstract 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.https://doi.org/10.1007/JHEP03(2023)112Classical Theories of GravityScattering Amplitudes |
| spellingShingle | Kyoungho Cho Kwangeon Kim Kanghoon Lee Perturbations of general relativity to all orders and the general n th order terms Journal of High Energy Physics Classical Theories of Gravity Scattering Amplitudes |
| title | Perturbations of general relativity to all orders and the general n th order terms |
| title_full | Perturbations of general relativity to all orders and the general n th order terms |
| title_fullStr | Perturbations of general relativity to all orders and the general n th order terms |
| title_full_unstemmed | Perturbations of general relativity to all orders and the general n th order terms |
| title_short | Perturbations of general relativity to all orders and the general n th order terms |
| title_sort | perturbations of general relativity to all orders and the general n th order terms |
| topic | Classical Theories of Gravity Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP03(2023)112 |
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