The theory of caustics and wave front singularities with physical applications

DOI10.1063/1.533316zbMath0974.58037arXivgr-qc/9906065OpenAlexW1968468310MaRDI QIDQ2738013

Jürgen Ehlers, Ezra T. Newman

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/gr-qc/9906065

zbMATH Keywords

singularitiesLagrangian submanifoldsHamilton-Jacobi theoryeikonal equationcausticswave frontsLegendrian submanifoldsnull surfaces

Mathematics Subject Classification ID

General relativity (83C99) Contact manifolds (general theory) (53D10) Lagrangian submanifolds; Maslov index (53D12) Catastrophe theory (58K35) Geometric optics (78A05)

Related Items

Wavefronts, caustic sheets, and caustic surfing in gravitational lensing, Symplectic scattering approach to gravitational lensing, Evolutes of fronts in the Euclidean plane, Null geodesics and wave front singularities in the Gödel space-time, Mathematics of gravitational lensing: Multiple imaging and magnification, Examining the Kerr metric through wave fronts of null geodesics, On caustics of submanifolds and canal hypersurfaces in Euclidean space, An asymptotic universal focal decomposition for non-isochronous potentials, A spinor reformulation of the null surface treatment of GR, A finite dimensional approach to light rays in general relativity, The Hawking energy on the past lightcone in cosmology, On the Last Geometric Statement of Jacobi, Caustics of translation surfaces in Euclidean 3-space, Gravitational lensing from a spacetime perspective, Jacobi’s last geometric statement extends to a wider class of Liouville surfaces, On families of Lagrangian submanifolds, The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

Cites Work

• Topological problems of the theory of wave propagation
• Arnold’s singularity theory and gravitational lensing
• Characteristic initial data and wavefront singularities in general relativity
• The Eikonal equation in flat space: Null surfaces and their singularities. I
• The Eikonal equation in asymptotically flat space–times
• On the dynamics of characteristic surfaces
• GR via characteristic surfaces
• Caustics of wavefronts in general relativity