Shapovalov wave-like spacetimes

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 of space 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.

17 pages

References in corpus (4)

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• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method

Cited by in corpus (16)

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• Exact models of pure radiation in R^2 gravity for spatially homogeneous Shapovalov spacetimes type II
• Type I Shapovalov wave spacetimes in the Brans-Dicke scalar-tensor theory of gravity
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• Wave-like exact models with symmetry of spatial homogeneity in the quadratic theory of gravity with a scalar field
• Secondary gravitational waves against a strong gravitational wave in the Bianchi VI universe
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