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[Licence| Download | New Version Template] aeex_v3_0.tar.gz(6804 Kbytes)
Manuscript Title: Motion4D-library extended
Authors: Thomas Müller
Program title: Motion4D-library
Catalogue identifier: AEEX_v3_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)1386
Programming language: C++.
Computer: All platforms with a C++ compiler.
Operating system: Linux, Windows.
RAM: 61 MBytes
Supplementary material: A document containing a summary of the revisions is available.
Keywords: general relativity, timelike and lightlike geodesics, Sachs basis, Jacobi equation.
Classification: 1.5.

External routines: Gnu Scientic Library (GSL) (http://www.gnu.org/software/gsl/)

Does the new version supersede the previous version?: Yes

Nature of problem:
Solve geodesic equation, parallel and Fermi-Walker transport in four-dimensional Lorentzian spacetimes. Determine gravitational lensing by integration of Jacobi equation and parallel transport of Sachs basis.

Solution method:
Integration of ordinary differential equations.

Reasons for new version:
The main novelty of the current version is the extension to integrate the Jacobi equation and the parallel transport of the Sachs basis along null geodesics. In combination, the change of the cross section of a light bundle and thus the gravitational lensing effect of a spacetime can be determined. Furthermore, we have implemented several new metrics

Summary of revisions:
See Supplementary material, above.

Running time:
The test runs provided with the distribution require only a few seconds to run.

References:
[1] T. Müller. New version announcement to the GeodesicViewer (http://cpc.cs.qub.ac.uk/summaries/AEFP_v2_0.html).
[2] P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses (Springer, 1992).
[3] W. Rindler, Phys. Lett. A 245, 363 (1998).
[4] D. Kramer, Ann. Phys. 9, 331 (2000).
[5] F. J. Ernst, J. Math. Phys. 17, 54 (1976).
[6] S. Chandrasekhar, Proc. R. Soc. Lond. A 421, 227 (1989).
[7] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of the Einstein Field Equations (Cambridge University Press, 2009).
[8] A. I. Janis, E. T. Newman, and J. Winicour, Phys. Rev. Lett. 20, 878 (1968).
[9] K. Martel and E. Poisson, Am. J. Phys. 69,476 (2001).
[10] W. Rindler. Relativity - Special, General, and Cosmology (Oxford University Press, Oxford, 2007).
[11] C. W. Misner, K.S. Thorne, and J.A. Wheeler. Gravitation (W. H. Freeman, 1973).
[12] J. Sultana and C. C. Dyer, Gen. Relativ. Gravit. 37, 1349 (2005).
[13] D. Bini, C. Cherubini, and Robert T. Jantzen, Class. Quantum Grav. 19, 5481 (2002).
[14] T. Muller and F. Grave, arXiv:0904.4184 [gr-qc].