Cadabra and python algorithms in general relativity and cosmology I: Generalities
DOI:
https://doi.org/10.31349/RevMexFisE.22.010202Keywords:
Computer Algebra Systems, Cadabra, Gravitation, Classical Field TheoryAbstract
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight the way in which Cadabra's philosophy differs from other systems with related functionality. The use of various new built-in packages is discussed, and we show how such packages can also be created by end-users directly using the notebook interface.
The current paper focuses on fairly generic applications in gravitational theories, including the use of differential forms, the derivation of field equations and the construction of their solutions.
References
M. A. H. MacCallum, Computer algebra in gravity research, Living Rev. Rel. 21 (2018) 6, https://doi.org/10.1007/s41114-018-0015-6
K. Peeters, Cadabra: a Field-Theory Motivated Symbolic Computer Algebra System, Comput. Phys. Commun. 176 (2007) 550, https://doi.org/10.1016/j.cpc.2007.01.003
K. Peeters, Introducing Cadabra: A Symbolic Computer Algebra System for Field Theory problems (2007). https://doi.org/10.48550/arXiv.hep-th/0701238
K. Peeters, Symbolic Field Theory With Cadabra, Computeralgebra Rundbrief 41 (2007) 16
K. Peeters, Cadabra2: computer algebra for field theory revisited, J. Open Source Softw. 3 (2018) 1118, https://doi.org/10.21105/joss.01118
V. V. Baran and D. S. Delion, Analytical approach for the quartet condensation model, Phys. Rev. C 99 (2019) 031303, https://doi.org/10.1103/PhysRevC.99.031303
O. Castillo-Felisola, D. T. Price, and M. Scomparin, Cadabra and Python algorithms in general relativity and cosmology II: Gravitational waves, Comput. Phys. Commun. 289 (2023) 108748, https://doi.org/10.1016/j.cpc.2023.108748
L. Brewin, Using Cadabra for Tensor Computations in General Relativity (2019), http://arxiv.org/abs/1912.08839v1
A. Einstein, Zur Allgemeinen Relativitätstheorie, Sitzungsber. Preuss. Akad. Wiss. 1 (1915) 778
A. Einstein, Die Grundlage Der Allgemeinen Relativitätstheorie, Ann. Phys. 49 (1916) 284
K. Peeters, Cadabra manual pages, https://cadabra.science/man.html
A. Meurer et al., Sympy: Symbolic Computing in Python, PeerJ Computer Science 3 (2017) e103, https://doi.org/10.7717/peerj-cs.103
C. Lanczos, A Remarkable Property of the Riemann- Christoffel Tensor in Four dimensions, Annals Math. (1938) 842
D. Lovelock, The Uniqueness of the Einstein Field Equations in a Four-Dimensional Space, Archive for Rational Mechanics and Analysis 33 (1969) 54, https://doi.org/10.1007/BF00248156
D. Lovelock, The Einstein Tensor and Its generalizations, J. Math. Phys. 12 (1971) 498, https://doi.org/10.1063/1.1665613
T. Padmanabhan and D. Kothawala, Lanczos-Lovelock Models of Gravity, Phys. Rep 531 (2013) 115, https://doi.org/10.1016/j.physrep.2013.05.007
F. Müeller-Hoissen, Spontaneous Compactification With Quadratic and Cubic Curvature Terms, Phys. Lett. B 163 (1985) 106, https://doi.org/10.1016/0370-2693(85)90202-3
F. Müeller-Hoissen, From Chern-Simons To Gauss-Bonnet, Nucl. Phys. B 346 (1990) 235, https://doi.org/10.1016/0550-3213(90)90246-A
T. Verwimp, On Higher Dimensional Gravity: the Lagrangian, Its Dimensional Reduction and a Cosmological Model, Class. Quantum Grav. 6 (1989) 1655, https://doi.org/10.1088/0264-9381/6/11/018
J. T. Jebsen, Ark. Mat. Ast. Fys. 15 (1921)
G. D. Birkhoff, Relativity and Modern Physics (Harvard University Press, 1923)
W. Alexandrow, Ann. Der Phys. 72 (1923) 141
J. Eisland, Trans. Amer. Math. Soc. 23 (1925) 213
L. Brewin, hybrid-latex, (2019).https://github.com/ leo-brewin/hybrid-latex.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 O. Castillo-Felisola, D. T. Price, M. Scomparin
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
