Journal ArticleDOI
Singular manifold analysis of the Einstein vacuum field equations
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In this paper, the authors investigated the Painleve property of the vacuum Einstein field equations and observed that the field equations possess this property when spacetime admits commuting, non-null two Killing vector fields.Abstract:
The Painleve property of the vacuum Einstein field equations is investigated. It is observed that the field equations possess this property when spacetime admits commuting, nonnull two Killing vector fields.read more
References
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Journal ArticleDOI
The classical theory of fields
TL;DR: The principle of relativity Relativistic mechanics Electromagnetic fields electromagnetic waves as discussed by the authors The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation
Book
The Large Scale Structure of Space-Time
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
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Exact Solutions of Einstein's Field Equations
TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.
Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
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