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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Deformed surfaces in holographic interferometry. Similar aspects in general gravitational fields; pp. 34–47

(Full article in PDF format) doi: 10.3176/proc.2008.1.04


Authors

Walter Schumann

Abstract

In the introductory part (Section 1) some aspects of the large deformation analysis in holographic interferometry are briefly outlined. The calculus there may also serve as an introduction for a link to the principal part afterwards. Modifications of the set-up at the reconstruction should recover the previously invisible fringes. Their spacing and the contrast are characterized by the fringe and visibility vectors. The relevant derivative of the path difference involves the polar decomposition of the deformation gradient into strain and rotation and the image aberration implies further changes of the geodesic curvature and of surface curvatures. In the principal part (sections 2, 3, 4) these considerations lead then to similar aspects for hypersurfaces, above all to an interpretation of gravitation by two virtual deformations for the Schwarzschild solution. This is further useful for non-spherical gravitational fields, for the invariants there, and for the TOV relation between pressure and density. The null-geodesics or light rays can also be interpreted by these virtual deformations. An approach towards the Kerr solution for rotating stars is added. As to linearization, a connection is outlined, which confirms the non-existence of gravitational waves if they are described by pure geometrical considerations of the field equations. Detailed equations for calculations are presented in Section 4.

Keywords

optics holographic interferometry, large deformations, curved (hyper-) surfaces, general gravitational fields.

References

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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December