The basic idea is that we may regard the normal line as a ray emanate from the curve or, the surface , so that the evolute can be considered as a caustic in geometrical optics. This case the normal lines of a timelike surface are spacelike, so these are not corresponding to rays in the physical sense.
Therefore, the Lorentz evolute is not a caustic in the sense of geometric optics. The set of critical values of the light sheet is called a lightlike focal curve along a spacelike curve. Actually, the notion of light sheets is important in Physics which provides models of several kinds of horizons in space-times . Each spacelike curve is called a momentary curve. We consider the family of lightlike surfaces along momentary curves in the world sheet.
The locus of the singularities the lightlike focal curves of lightlike surfaces along momentary curves form a caustic. This construction is originally from the theoretical physics the string theory, the brane world scenario, the cosmology, and so on [3, 4].
optics - Explanation of ray caustics in E&M - Physics Stack Exchange
Moreover, we have no notion of the time constant in the relativity theory. Hence everything that is moving depends on the time.
Therefore, we consider world sheets in the relativity theory. We remark that we have results for higher dimensional cases and for other Lorentz space-forms similar to this special case [8, 9].
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Volume I: the classification of critical points, caustics and wave fronts. Waves in layered media. London: Academic Press.
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The holographic principle. Holographic domains of ant-de Sitter space. The mathematical theory of black holes. International Series of Monographs on Physics. Fourier integral operators I. Sci, Vol.
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