Orthogonal transitivity, invertibility and null geodesic separability in type D vacuum solutions of Einstein’s field equations with cosmological constant

DOI10.1063/1.525273zbMath0495.53023OpenAlexW4248940350MaRDI QIDQ3959059

Stephanie R. Czapor, Raymond G. Mclenaghan

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1063/1.525273

zbMATH Keywords

Hamilton-Jacobi equationcosmological constantKilling tensorlocal isometriesgroup orbitsPetrov type-D vacuum solutionsprincipal null congruences

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Applications of local differential geometry to the sciences (53B50)

Related Items (7)

Unnamed Item ⋮ Separation of variables and symmetry operators for the neutrino and Dirac equations in the space-times admitting a two-parameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences ⋮ Type D vacuum solutions: a new intrinsic approach ⋮ The automatic conversion of spinor equations to dyad form in MAPLE ⋮ Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields ⋮ NP: A maple package for performing calculations in the Newman-Penrose formalism ⋮ Separation of variables and quantum numbers for Weyl neutrino fields on curved space-time

Cites Work

• Riemannian-Maxwellian invertible structures in general relativity
• Separability structures and Killing-Yano tensors in vacuum type-D space- times without acceleration
• Killing tensors and the separation of the Hamilton-Jacobi equation
• On the relationship between Killing tensors and Killing-Yano tensors
• On quadratic first integrals of the geodesic equations for type [22 spacetimes]
• Spacetimes with Killing tensors
• The symmetries of Kerr black holes
• Uniform Electromagnetic Field in the Theory of General Relativity
• An Approach to Gravitational Radiation by a Method of Spin Coefficients
• Type-D space-times with a Killing tensor
• Orthogonal transitivity, invertibility, and null geodesic separability in type D electrovac solutions of Einstein’s field equations with cosmological constant
• Diverging type-D metrics
• Global Structure of the Kerr Family of Gravitational Fields
• Type D Vacuum Metrics
• Generalization of a Theorem by Goldberg and Sachs

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