The \v{d}Alembert solution in hyperboloidal foliations
Abstract
We explicitly construct the analogue of the \v{d}Alembert solution to the 1+1 wave equation in an hyperboloidal setting. This hyperboloidal \v{d}Alembert solution is used, in turn, to gain intuition into the behaviour of solutions to the wave equation in a hyperboloidal foliation and to explain some apparently anomalous behaviour observed in numerically constructed solutions discussed in the literature.
Keywords
Cite
@article{arxiv.2403.07045,
title = {The \v{d}Alembert solution in hyperboloidal foliations},
author = {Juan A. Valiente Kroon and Lidia J. Gomes Da Silva},
journal= {arXiv preprint arXiv:2403.07045},
year = {2024}
}
Comments
21 pages, 10 figures; Amended to accommodate for referees requests and published version: important typo in Eqs.(12,13) corrected, and Appendix added with further examples in different hyperboloidal coordinate charts; Part of the topical collection "Hyperboloidal foliations in the era of gravitational-wave astronomy: from mathematical relativity to astrophysics"