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[Licence| Download | New Version Template] aeex_v3_1.tar.gz(6648 Kbytes)
Manuscript Title: Motion4D-library extended
Authors: Thomas Müller
Program title: Motion4D-library
Catalogue identifier: AEEX_v3_1
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)2798
Programming language: C++.
Computer: All platforms with a C++ compiler.
Operating system: Linux, Windows.
RAM: 61 MBytes
Keywords: General relativity, Timelike and lightlike geodesics, Sachs basis, Jacobi equation.
PACS: 04.20.-q, 04.25.D-, 04.20.Ex.
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 reason for the new version is the update of some methods to work with the four-dimensional ray tracing code GeoViS. Furthermore, some new metrics and integrators were implemented.

Summary of revisions:
The four-dimensional ray tracing code GeoViS [1] is based on the Motion4D library. All of the metrics and geodesic integrators of the library can be accessed by means of GeoViS ' scheme-based scripting language. For that, some methods had to be updated.
In the following, a list of newly implemented metrics is given:
  • AlcubierreSimple: This metric uses a simplified warp bubble function compared to the original one by Alcubierre [2], see McMonigal et al. [3].
  • ChazyCurzonRot: The metric of the rotational Chazy-Curzon solution is taken from Stephani et al. [4].
  • Curzon: The Curzon metric in cylindrical coordinates is taken from Scott and Szekeres [5].
  • EinsteinRosenWaveWWB: A detailed discussion of the Einstein-Rosen wave with a Weber-Wheeler-Bonnor pulse can be found in Griffiths and Micciche [6].
  • ErezRosenVar: The original Erez-Rosen metric is quite intricate, see e.g. Krori and Sarmah [7]. Hence, we use here a reduced version with a simpler quadrupole term.
  • KastorTraschen: The Kastor-Traschen metric with two black holes is taken from Griffiths and Podolský [8]
Furthermore, the Dormand-Prince 5(4) and 6(5) integrators taken from Guthmann [8] were implemented.

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

[1] T. Müller, GeoViS - Relativistic ray tracing in four-dimensional spacetimes, accepted for publication in Computer Physics Communications.
[2] M. Alcubierre, Classical Quantum Gravity 11, L73 (1994).
[3] B. McMonigal, G. F. Lewis, and P. O'Byrne, Physical Review D 85, 064024 (2012).
[4] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of the Einstein Field Equations (Cambridge University Press, 2009).
[5] Susan M. Scott and P. Szekeres, Gen. Relativ. Gravit. 18, 557 (1986).
[6] J. B. Griffiths and S. Micciche, Physics Letters A 223, 37 (1997).
[7] K. D. Krori and I. C. Sarmah, Gen. Relativ. Gravit. 23, 801 (1991).
[8] J. B. Griffiths and J. Podolský, Exact Space-Times in Einstein's General Relativity (Cambridge University Press, 2009).
[8] A. Guthmann, Einführung in die Himmelsmechanik und Ephemeridenrechnung (Spektrum Verlag, 2000, german).