Infinite dimensional Morse theory and Fermat’s principle in general relativity. I
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Publication:4873415
DOI10.1063/1.531198zbMath0854.58014OpenAlexW2031900677MaRDI QIDQ4873415
Publication date: 22 January 1997
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.531198
variational problemgeneral relativityinfinite dimensional Morse theoryFermat's principlegravitational lens effect
Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Variational principles of physics (49S05)
Related Items
On a Fermat principle in general relativity. A Morse theory for light rays, A timelike extension of Fermat's principle in general relativity and applications, Geodesic connectedness in generalized Reissner-Nordström type Lorentz manifolds, A local variational theory for the Schmidt metric, Mathematics of gravitational lensing: Multiple imaging and magnification, Unnamed Item, On a morse theory for light rays without nondegeneracy assumptions, A timelike extension of fermat's principle in general relativity. Comparisons with the lightlike case, Fermats principle, Morse theory and applications to the gravitational lens effect, Fermat principle in Finsler spacetimes, Gravitational lensing from a spacetime perspective, Genericity of nondegeneracy for light rays in stationary spacetimes, Functional regularity properties for light rays in general relativity, A general-relativistic Fermat principle for extended light sources and extended receivers, On a Fermat principle in general relativity. A Ljusternik-Schnirelmann theory for light rays, Light rays having extreme points with the same spatial coordinates
Cites Work
- A Morse index theorem for null geodesics
- A Morse theory for geodesics on a Lorentz manifold
- Erratum of J. Everson and C. J. Talbot: Morse theory on timelike and causal curves
- A Fermat principle for stationary space-times and applications to light rays
- Morse theory and a non-linear generalization of the Dirichlet problem
- Morse theory on Hilbert manifolds
- On Fermat's principle in general relativity. I. The general case
- A gravitational lens produces an odd number of images
- A generalized Morse theory
