Classification of Einstein spaces with Stackel metric of type (3.0)

2025/04/15 by V. V. Obukhov, Obukhov, V. V. · 1 citation
Mathematics · Physics and Astronomy · #70H20 #83C05 #83C15 #83C20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.2504.11084

openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classification of the Einstein spaces with the Stackel metric of the (3.0) has been done. These spaces are invariant under the action of the three-parameter abelian group of motions and belong to the first type Bianchi spaces. Thus the classification of vacuum and electrovacuum Stackel spaces of all types is completed and the complete list of metrics of such spaces in privileged coordinate systems is given.

Citations

• Exact solutions of Maxwell equations in homogeneous spaces with the group of motions G₃(VIII)
• Exact solutions of Maxwell equations in homogeneous spaces with group of motions G₃(IX)
• Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions G₃ act transitively on null subsurfaces of spacetime
• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Algebra of symmetry operators for Klein-Gordon-Fock equation
• Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)
• Noncommutative integration of the Dirac equation in homogeneous spaces
• Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)
• Exact solutions of the Klein-Gordon equation in external electromagnetic fields on 3D de Sitter background
• Wave-like spatially homogeneous models of Stackel spacetimes (2.1) type in the scalar-tensor theory of gravity
• Constructing a complete integral of the Hamilton-Jacobi equation on pseudo-Riemannian spaces with simply transitive groups of motions
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The space-time models with dust matter that admit separation of variables in Hamilton-Jacobi equations of a test particle
• Cosmological Models Coupled with Dark Matter in a Dissipative Universe
• Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• Multiple ΛCDM cosmology with string landscape features and future singularities
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Four-dimensional pseudo-Riemannian homogeneous Ricci solitons
• Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
• Exact Solutions of Einstein's Field Equations
• Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
• Geometrical Theorems on Einstein's Cosmological Equations
• Sulla integrazione della equazione di Hamilton-Jacobi per separazione di variabili
• Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie

Cited by

• Exact solutions of Maxwell vacuum equations in Petrov homogeneous non-null spaces

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