{"title":"A note on diffeomorphism-invariance in gravitational field equations","authors":"S C Tiwari","doi":"arxiv-2408.05229","DOIUrl":null,"url":null,"abstract":"The notion of diffeomorphism invariance and general covariance are\nconceptually delicate issues for the field equations and the actions. A\nthorough study on the original Einstein field equation and its two\nmodifications by Einstein is presented. It is concluded that the cosmological\nconstant and the unimodular condition are independent concepts, and the\nunimodular condition has no direct role in the derivation of the traceless\nfield equation. Unimodular gravity with unambiguous action does not exist, and\nthe derivation of traceless equation from the action principle is an open\nquestion.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - General Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.05229","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The notion of diffeomorphism invariance and general covariance are
conceptually delicate issues for the field equations and the actions. A
thorough study on the original Einstein field equation and its two
modifications by Einstein is presented. It is concluded that the cosmological
constant and the unimodular condition are independent concepts, and the
unimodular condition has no direct role in the derivation of the traceless
field equation. Unimodular gravity with unambiguous action does not exist, and
the derivation of traceless equation from the action principle is an open
question.
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