Shapovalov Wave-Like Spacetimes
К. Е. Осетрин, Evgeny Osetrin
Abstract
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.
Topics & Concepts
Eikonal equationSeparation of variablesHamilton–Jacobi equationWave equationPhysicsIsotropyMetric (unit)Test particleMathematical analysisMathematical physicsSpace (punctuation)Variable (mathematics)Motion (physics)EinsteinClassical mechanicsConstant (computer programming)MathematicsQuantum mechanicsPartial differential equationComputer scienceProgramming languageOperations managementEconomicsOperating systemCosmology and Gravitation TheoriesAdvanced Differential Geometry ResearchBlack Holes and Theoretical Physics