ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

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

Author
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.
References

  1. Champagne, E. B. Holographic interferometry extended. In Digest of Papers, Int. Opt. Computing Conf., Zurich (IEEE, New York). 1974, 73–74.

  2. Cuche, D. E. Modification methods in holographic and speckle interferometry. In Interferometry in Speckle Light (Jacquot, P. and Fournier, J. M., eds). Springer, Berlin, Heidelberg, New York, 2000, 109–114.

  3. Stetson, K. A. Fringe interpretation for hologram interferometry of rigid-body motions and homogenous deformations. J. Opt. Soc. Am., 1974, 64, 1–10.

  4. Walles, S. Visibility and localization of fringes in holographic interferometry of diffusely reflecting surfaces. Ark. Fys., 1970, 40, 299–403.

  5. Schwarzschild, K. Ueber das Gravitationsfeld eines Massenpunktes. Sitzungsberichte der deutschen Akademie der Wissen­schaften, Kl. Math.-Phys. Tech. Berlin, 1916, 189–196.

  6. Misner, C. W., Thorne, K. S. and Wheeler, J. A. Gravitation. W. H. Freeman and Company, New York, 1972.

  7. Plebanski, J. and Krasinski, A. An Introduction to General Relativity and Cosmology. Cambridge University Press, 2007, 196–200.

  8. Sexl, R. U. and Urbantke, H. K. Gravitation und Kosmologie. 2nd edn. Wissenschaftsverlag, Wien, 1981, 53 and 240–243.

  9. Kerr, R. P. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett., 1963, 11(5), 237–238.
doi:10.1103/PhysRevLett.11.237

10. Goenner, H. Einführung in die spezielle und allgemeine Relativitätstheorie. Spektrum, Akademischer Verlag, Heidelberg, Oxford, 1996, 145–149 and 304.

11. Penrose, R. Structure of space-time. In Battelle Rencontres 1967 (Dewitt, C. M. and Wheeler, J. A., eds). Benjamin, New York, Amsterdam, 1968, 121–235.

12. Poisson, E. A Relativist’s Toolkit. Cambridge University Press, 2004.
Back to Issue