JMP  Vol.3 No.12 , December 2012
Wavefronts and Light Cones for Kerr Spacetimes
ABSTRACT
We investigate the light propagation by means of simulations of wavefronts and light cones for Kerr spacetimes. Simulations of this kind give us a new insight to better understand the light propagation in presence of massive rotating black holes. A relevant result is that wavefronts are backscattered with winding around the black hole. To generate these visualizations, an interactive computer program with a graphical user interface, called JWFront, was written in Java.

Cite this paper
F. Frutos-Alfaro, F. Grave, T. Müller and D. Adis, "Wavefronts and Light Cones for Kerr Spacetimes," Journal of Modern Physics, Vol. 3 No. 12, 2012, pp. 1882-1890. doi: 10.4236/jmp.2012.312237.
References
[1]   R. P. Kerr, “Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics,” Physical Review Letters, Vol. 11, No. 5, 1963, p. 237. doi:10.1103/PhysRevLett.11.237

[2]   H. Friedrich and J. M. Stewart, “Characteristic Initial Data and Wavefront Singularities in General Relativity,” Proceedings of the Royal Society London, Series A, Vol. 385, No. 1789, 1983, pp. 345-371.

[3]   J. M. Stewart, “Advanced General Relativity,” Cambridge Monographs on Mathematical Physics, Cambridge University, Cambridge, 1993.

[4]   V. I. Arnold, “Singularities of Caustics and Wavefronts,” Kluwer, Amsterdam, 1990. doi:10.1007/978-94-011-3330-2

[5]   W. Hasse, M. Kriele and V. Perlick, “Caustics of Wave-fronts in General Relativity,” Classical and Quantum Gravity, Vol. 13, No. 5, 1996, pp. 1161-1182. doi:10.1088/0264-9381/13/5/027

[6]   R. Low, “Stable Singularities of Wavefronts in General Relativity,” Journal of Mathematical Physics, Vol. 36, No. 8, 1998, pp. 3332-3335. doi:10.1063/1.532257

[7]   J. Ehlers and E. Newman, “The Theory of Caustics and Wavefront Singularities with Physical Applications,” Journal of Mathematical Physics, Vol. 41, 2000, pp. 3344-3378, arXiv:gr-qc/9906065. doi:10.1063/1.533316

[8]   V. Perlick, “Gravitational Lensing from a Spacetime Perspective,” Living Reviews in Relativity, Vol. 7, No. 9, 2004, arXiv:1010.3416.

[9]   K. P. Rauch and R. Blandford, “Optical Caustics in a Kerr Spacetime and the Origin of Rapid X-Ray Variability in Active Galactic Nuclei,” The Astrophysical Journal, Vol. 421, No. 1, 1994, pp. 46-68. doi:10.1086/173625

[10]   F. Grave, “Visualization of Gravitational Collapse and Wavefronts in the General Relativity Theory, Diplomar-beit,” Master Thesis, Eberhard Karls Universit?t Tübingen, Tübingen, 2004.

[11]   M. Sereno and F. De Luca, “Primary Caustics and Critical Points behind a Kerr Black Hole,” Physical Review D, Vol. 78, No. 2, 2008, Article ID: 023008, arXiv: astro-ph/0710.5923.

[12]   V. Bozza, “Optical Caustics of Kerr Spacetime: The Full Structure,” Physical Review D, Vol. 78, No. 6, 2008, Article ID: 063014, arXiv:gr-qc/0806.4102.

[13]   R. D. Blandford and R. Narayan, “Cosmological Applications of Gravitational Lensing,” Annual Review of Astronomy and Astrophysics, Vol. 30, 1992, pp. 311-358. doi:10.1146/annurev.aa.30.090192.001523

[14]   P. Schneider, J. Ehlers and E. E. Falco, “Gravitational Lenses,” Springer, Berlin, 1992. doi:10.1007/978-1-4612-2756-4

[15]   H. Ohanian and R. Ruffini, “Gravitation and Spacetime,” W. W. Norton & Company, New York, 1994.

[16]   A. O. Petters, “Arnold’s Singularity Theory and Gravitational Lensing,” Journal of Mathematical Physics, Vol. 34, No. 8, 1993, pp. 3555-3581. doi:10.1063/1.530045

[17]   A. O. Petters, H. Levine and J. Wambsganss, “Singularity Theory and Gravitational Lensing,” Springer, Berlin, 2001. doi:10.1007/978-1-4612-0145-8

[18]   S. Frittelli and A. O. Petters. “Wave Fronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing,” Journal of Mathematical Physics, Vol. 43, No. 11, 2002, pp. 5578-5611, arXiv:astro-ph/0208135. doi:10.1063/1.1511790

[19]   G. F. R. Ellis, B. A. Bassett and P. K. S. Dunsby, “Lensing and Caustic Effects on Cosmological Distances,” Classical and Quantum Gravity, Vol. 15, No. 8, 1998, pp. 2345-2361, arXiv:gr-qc/9801092v1. doi:10.1088/0264-9381/15/8/015

[20]   F. Grave, F. Frutos-Alfaro, T. Müller and D. Adis, “JWFront in the Eleventh Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity,” In: H. Kleinert and R. T. Jantzen, Eds., Gravitation and Relativistic Field Theories, Proceedings of the MG11 Meeting, World Scientific Publishing Company, London, 2008.

[21]   R. d’Inverno, “Introducing Einstein’s Relativity,” Oxford University Press, Oxford, 1992.

[22]   C. W. Misner, K. S. Thorne and J. A. Wheeler, “Gravitation,” Freeman, San Francisco, 1973.

[23]   J. M. Bardeen, W. H. Press and S. A. Teukolsky, “Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation,” The Astrophysical Journal, Vol. 178, 1972, pp. 347-369. doi:10.1086/151796

[24]   A. C. Hearn, “REDUCE (User’s and Contributed Packages Manual),” Konrad-Zuse-Zentrum für Information-stechnik, Berlin, 1999.

[25]   O. Semerák, “Spinning Test Particles in a Kerr Field-I,” Monthly Notices of Royal Astronomical Society, Vol. 308, No. 3, 1999, pp. 863-875. doi:10.1046/j.1365-8711.1999.02754.x

 
 
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