The new version of the Motion4D library is mainly an update to work with the four-dimensional ray tracing code GeoViS which makes full use of all the implemented metrics and geodesic integrators.Program title: Motion4D-libraryCatalogue identifier: AEEX_v3_1Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEX_v3_1.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 189793No. of bytes in distributed program, including test data, etc.: 6808546Distribution format: tar.gzProgramming language: C++.Computer: All platforms with a C++ compiler.Operating system: Linux, Windows.RAM: 61 MBytesClassification: 1.5.Catalogue identifier of previous version: AEEX_v3_0Journal reference of previous version: Comput. Phys. Comm. 182(2011)1386External routines: GNU Scientific Library (GSL) (http://www.gnu.org/software/gsl/)Does the new version supersede the previous version?: YesNature 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:
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AlcubierreSimple: This metric uses a simplified warp bubble function compared to the original one by Alcubierre [2], see McMonigal et al. [3].
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ChazyCurzonRot: The metric of the rotational Chazy–Curzon solution is taken from Stephani et al. [4].
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Curzon: The Curzon metric in cylindrical coordinates is taken from Scott and Szekeres [5].
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EinsteinRosenWaveWWB: A detailed discussion of the Einstein–Rosen wave with a Weber–Wheeler–Bonnor pulse can be found in Griffiths and Micciche [6].
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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.
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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.References:
- [1]
T. Müller, GeoViS - Relativistic ray tracing in four-dimensional spacetimes, Computer Physics Communications 185, 2301 (2014).
- [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).
- [9]
A. Guthmann, Einführung in die Himmelsmechanik und Ephemeridenrechnung (Spektrum Verlag, 2000, german).