Publication: Geometric inequivalence of metric and Palatini formulations of General Relativity
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2020-03-10
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Elsevier Science BV
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Abstract
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K (R beta mu nu R alpha beta mu nu)-R-alpha, can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the connection. (C) 2020 The Author(s). Published by Elsevier B.V.
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© 2020 The Author(s).
C. B. is funded by the National Scientific and Technical Research Council (CONICET). AD and AJC are supported by a PhD contract of the program FPU 2015 (Spanish Ministry of Economy and Competitiveness) with references FPU15/05406 and FPU15/02864, respectively. GJO is funded by the Ramon y Cajal contract RYC-2013-13019 (Spain). DRG is funded by the Atraccion de Talento Investigadorprogramme of the Comunidad de Madrid No. 2018-T1/TIC-10431, and acknowledges support from the Fundacao para a Ciencia e a Tecnologia (FCT, Portugal) research grants Nos. PTDC/FIS-OUT/29048/2017 and PTDC/FIS-PAR/31938/2017. Thiswork is supported by the Spanish projects FIS2017-84440-C2-1-P, FIS2014-57387-C3-1-P (MINECO/FEDER, EU) and i-LINK1215 (CSIC), the project H2020-MSCA-RISE-2017 Grant FunFiCO-777740, the project SEJI/2017/042 (Generalitat Valenciana), the Consolider Program CPANPHY-1205388, and the Severo Ochoa grant SEV2014-0398 (Spain). This article is based upon work from COST Action CA15117, supported by COST (European Cooperation in Science and Technology).