Notebook for decomposing the source of the Teukolsky equation analytically. The notebook sets up the Held formalism.
Notebook adapted and built on from "The N.P. and G.H.P. formalisms." Alfonso García-Parrado Gómez-Lobo, Universidade do Minho, Portugal, September 2009, http://www.xact.es/Documentation/English/PublicNPGHP.nb.
The specific parts of this notebook which were adapted from "The N.P. and G.H.P. formalisms." are the "Newman Penrose Formalism" (apart from the Teukolsky derivation sections) and "GHP Formalism" chapters in the "Set up Notebook" section. The rest of this notebook was created by the author, Andrew Spiers.
Notebook adapted and built on from "The N.P. and G.H.P. formalisms." Alfonso García-Parrado Gómez-Lobo, Universidade do Minho, Portugal, September 2009, http://www.xact.es/Documentation/English/PublicNPGHP.nb and "NP-and-GHP-Formalisms-for-2nd-order-Teukolsky" Andrew Spiers, University of Nottingham, 2023.
Author: Andrew Spiers [email protected] https://github.com/DrAndrewSpiers Department of Mathematical Sciences, University of Nottingham. 18/01/2024 Teukolsky-equation-source-decomposer.nb provides an example for decomposing the source of the Teukolsky equation using the half-Held formalism. Held-formalism.nb is provided for those interested in the full Held formalism. They are both only consistent in the Kinnersley tetrad.
Notebooks created in Mathematica 13.2
If you use this notebook for research please cite the accompanying paper:
Title: Efficiently Separating the Source of the Teukolsky Equation Authors: Andrew Spiers Year: 2024
Also, please cite the original notebooks Example bibtex: @misc{npnotebook, author = {A Garc'ia-Parrado G'omez-Lobo}, title = {The N.P. and G.H.P. formalisms.}, year = {2009}, howpublished = {http://www.xact.es/Documentation/English/PublicNPGHP.nb}, organization = {Universidade do Minho}, location = { Portugal}, }
and cite
@article{Spiers:2024src, author = "Spiers, Andrew", title = "{Analytically separating the source of the Teukolsky equation}", eprint = "2402.00604", archivePrefix = "arXiv", primaryClass = "gr-qc", doi = "10.1103/PhysRevD.109.104059", journal = "Phys. Rev. D", volume = "109", number = "10", pages = "104059", year = "2024" }
Held, Alan. "A formalism for the investigation of algebraically special metrics. I." Communications in Mathematical Physics 37 (1974): 311-326. Newman, Ezra, and Roger Penrose. "An approach to gravitational radiation by a method of spin coefficients." Journal of Mathematical Physics 3.3 (1962): 566-578. S . Teukolsky, The Astrophysical Journal, 185 : 635 - 647, 1973 October 15 S. Chandrasekhar's, The Mathematical theory of black holes, Clarendon Press, Oxford University Press, 1983 Geroch, Robert, Alan Held, and Roger Penrose. "A space-time calculus based on pairs of null directions." Journal of Mathematical Physics 14.7 (1973): 874-881.