volume | PIER Journals

Abstract

It is shown that in hyperbolic spaces, an electromagnetic radiation experiences shifts in spectrum as a function of curvature and distance. The equation relating distance in hyperbolic space, its curvature, and spectral shift is derived by method of horospheres. The active nature of the Lobachevskian vacuum is discussed with applications to physics.

1. Beardon, A. F., Geometry of Discrete Groups, Springer Verlag 1983., 1983.

2. Buseman, H. and P. J. Kelly, Projective Geometry and Projective Metrics, Academic Press, 1953.

3. von Brzeski, J. G. and V. von Brzeski, "Intensity and polarization of light in Lobachevskian space," In preparation.. Google Scholar

4. Chernikov, N. A. and Preprint No. 723, Joint Institute for Nuclear Research (JINR) Dubna, No. Preprint 723, 1961 (in Russian)., 1961.

5. Chernikov, N. A., Doklady Academy of Sciences of USSR, 114, 1957.

6. Gelfand, I. M., M. I. Grayev, and N. Ya. Vilenkin, Generalized Functions, Vol. 5, Vol. 5, 1966.

7. Heintze, E. and H. Christoph, "Geometry of horospheres," J. Differential Geometry, Vol. 12, 481-491, 1997. Google Scholar

8. Helgason, S., "Geometric analysis on symmetric spaces," Math. Surveys and Monographs, Vol. 39, 1994. Google Scholar

9. Klein, F., Vorlesungen uber Nicht Euklidische Geometrie, AMS Chelsea Publishing, 2000.

10. Rosenfeld, B. A., A History of Non Euclidean Geometry, Springer Verlag, 1988.

11. Smorodinsky, Ya. A., "Kinematics and Lobachevskian geometry," Atomnaya Energia, Vol. 14, 1963. Google Scholar

12. Sternberg, S., Group Theory and Physics, Cambridge University Press, 1995.