6533b7cefe1ef96bd1257247
RESEARCH PRODUCT
Geometric inequivalence of metric and Palatini formulations of General Relativity
Gonzalo J. OlmoGonzalo J. OlmoAdrià DelhomDiego Rubiera-garciaAlejandro Jiménez-canoCecilia Bejaranosubject
General RelativityNuclear and High Energy PhysicsRiemann curvature tensorFísica-Modelos matemáticosGeneral relativityScalar (mathematics)FOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)01 natural sciencesGeneral Relativity and Quantum Cosmology//purl.org/becyt/ford/1 [https]symbols.namesakeGeneral Relativity and Quantum Cosmology0103 physical sciencesSchwarzschild metricFísica matemáticaGauge theoryTensorGeometric inequivalence010306 general physicsMathematical PhysicsMathematical physicsPhysics010308 nuclear & particles physicsKretschmann scalar//purl.org/becyt/ford/1.3 [https]Mathematical Physics (math-ph)lcsh:QC1-999Symmetry (physics)symbolslcsh:Physicsdescription
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 R , 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-03-01 | Physics Letters |