Classification and conformal symmetry in three-dimensional space–times

DOI10.1063/1.532815zbMath0947.83014OpenAlexW2053221479MaRDI QIDQ4701802

M. S. Capocci, Graham S. Hall

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532815

zbMATH Keywords

spacetimesLorentz metricsthree-dimensional manifoldsclassification of the Ricci and curvature tensorsSchouten-Cotton-York tensor

Mathematics Subject Classification ID

Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (6)

Characterization of the Killing and homothetic vector fields on Lorentzian pr-waves three-manifolds with recurrent curvature ⋮ Homogeneous Ricci almost solitons ⋮ Three-dimensional homogeneous Lorentzian Yamabe solitons ⋮ Classification of static spherically symmetric space-times in f(R) theory of gravity according to their conformal vector fields ⋮ Proper conformal Killing vectors in static plane symmetric space-times ⋮ Symmetries of Lorentzian three-manifolds with recurrent curvature

Cites Work

• Selfsimilar Lorentzian manifolds
• Three-dimensional space-times
• Homothetic transformations with fixed points in spacetime
• Conformal groups and conformally equivalent isometry groups
• Proper homothetic maps and fixed points
• Some remarks on symmetries and transformation groups in general relativity
• Conformal symmetries and fixed points in space-time
• Gravitational waves in general relativity. VI. The outgoing radiation condition
• Conformal vector fields in general relativity
• Curvature collineations in general relativity. I
• The classification of the Ricci tensor in general relativity theory
• Affine collineations in general relativity and their fixed point structure
• Zeros of conformal vector fields

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