Abstract
We have previously discussed the characteristics of the gravitational waves (GW) and have, theoretically, shown that, like the corresponding electromagnetic (EM) waves, they also demonstrate, under certain conditions, holographic properties. In this work we have expanded this discussion and show that the assumed gravitational holographic images may, theoretically, be related to another property of GW’s which is their possible relation to singular (or nonsingular) trapped surfaces. We also show that this possibility may be, theoretically, related even to weak GW’s.
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Abbott, B. et al. (2004). Analysis of first LIGO science data for stochastic gravitational waves, Physical Review D 69, 122004.
Abrahams, A. M. and Evans, C. R. (1992). Trapping a geon: Black hole formation by an imploding gravitational wave, Physical Review D 46, R4117.
Acernese, F. et al. (2002). Status of VIRGO, Classical Quantum Gravity 19, 1421.
Alcubierre, M., Allen, G., Brugmann, B., Lanfermann, G., Seidel, E., Suen, W. M., and Tobias, M. (2000). Gravitational collapse of gravitational waves in 3-D numerical relativity, Physical Review D 61, 041501.
Ando, M. and the TAMA collaboration (2002). Current status of TAMA, Classical Quantum Gravity 19, 1409.
Anninos, P., Masso, J., Seidel, E., Suen, W. M., and Tobias, M. (1997). Dynamics of gravitational waves in 3D: Formulations, methods and tests, Physical Review D 56, 842.
Arnowitt, R., Desser, S., and Misner, C. W. (1962). The dynamics of General Relativity, In: Gravitation: An Introduction to Current Research, Witten, L. (ed.), Wiley, New-York.
Bar, D. (2005). The gravitational wave holography, gr-qc/0509052, to be published in IJTP.
Beig, R. and Murchadha, N. O. (1991). Trapped surfaces due to concentration of gravitational radiation, Physical Review Letters 66, 2421.
Bergmann, P. G. (1976). Introduction to the Theory of Relativity, Dover, New York.
Bernstein, D., Hobill, D., Seidel, E., and Smarr, L. (1994). Initial data for the black hole plus Brill wave spacetime, Physical Review D 50, 3760.
Brill, D. and Lindquist, R. W. (1963). Interaction energy in Geometrodynamics, Physical Review 131, 471–476.
Brill, D. R. (1959). On the positive definite mass of the Bondi-Weber-Wheeler time-symmetric gravitational waves, Annals of Physics 7, 466.
Brill, D. R. (1964). Suppl. Nuovo. Cimento 2, 1–56.
Brill, D. R. and Hartle, J. B. (1964). Method of the self-consistent field in General Relativity and its application to the gravitational geon, Physical Review B 135, 271.
Collier, R. J., Burckhardt, C. B., and Lin, L.H. (1971). Optical Holography, Academic Press.
Danzmann, K. (1995). GEO-600 a 600-m laser interferometric gravitational wave antenna, In First Edoardo Amaldi Conference on Gravitational Wave Experiments, Coccia, E., Pizella, G., and Ronga, F., (eds.), World Scientific, Singapore.
Einstein, A. and Rosen, N. (1935). The particle problem in the general theory of relativity, Physical Review 48, 73.
Eppley, K. (1977). Evolution of time-symmetric gravitational waves: Initial data and apparent horizons, Physical Review D 16, 1609.
Finkelstein, D. and Rodriguez, E. (1984). Relativity of topology and dynamics, International Journal of Theoretical Physics 23, 1065–1098.
Gabor, D. (1948). A new microscopic Principle, Nature 161, 777.
Gabor, D. (1949). Microscopy by reconstructed wavefronts, Proceedings of the Royal Society A 197, 454.
Gabor, D. (1951). Microscopy by reconstructed wavefronts: II, Proceedings of the Royal Society B 64, 449.
Gentle, A. P. (1999). Simplical Brill wave initial data, gr-qc/9901071.
Gentle, A. P., Holz, D. E., and Miller, W. A. (1998). Apparent horizons in simplical Brill wave initial data, gr-qc/9812057.
Hawking, S. W. and Ellis, G. F. R. (1973). The Large Scale Structure of Spacetime, Cambridge, London.
Kuchar, K. (1970). Ground state functional of the linearized gravitational field, Journal of Mathematical Physics 11, 3322.
Kuchar, K. (1971). Canonical quantization of cylindrical gravitational waves, Physical Review D 4, 955.
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation, Freeman, San Francisco.
Miyama, S. M. (1981). Time evolution of pure gravitational wave, Progress in Theoretical Physics 65, 894.
Nakamura, T. (1984). General solutions of the linearized Einstein equations and initial data for 3-D time evolution of pure gravitational waves, Progress in Theoretical Physics 72, 746.
Sorkin, R. D. (1986). Topology change and monopole creation, Physical Review D 33, 978.
Spiegel, M. R. (1959). Vector Analysis, Schaum’s Outline Series, McGraw-hill, New-York.
Thorne, K. S. (1980a). Gravitational wave research: Current status and future prospect, Reviews of Modern Physics 52, 285.
Thorne, K. S. (1980b). Multipole expansions of gravitational radiation, Reviews of Modern Physics 52, 299.
Tipler, F. J. (1980). Singularities from colliding plane gravitational waves, Physical Review D 22, 2929.
Urtsever, U. (1988a). Singularities in the collisions of almost-plane gravitational waves, Physical Review D 38, 1731.
Urtsever, U. (1988b). Colliding almost-plane gravitational waves: Colliding plane waves and general properties of almost-plane wave spacetimes, Physical Review D 37, 2803.
Urtsever, U. (1989). Quantum field theory in a colliding plane-wave background, Physical Review D 40, 360.
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PACS: 42.40.-i, 04.20.Gz, 04.30.-w, 04.30.Nk.
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Bar, D. Gravitational Holography and Trapped Surfaces. Int J Theor Phys 46, 664–687 (2007). https://doi.org/10.1007/s10773-006-9232-y
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DOI: https://doi.org/10.1007/s10773-006-9232-y