The ďAlembert solution in hyperboloidal foliations
arXiv:2403.07045 · doi:10.1007/s10714-024-03272-2
Abstract
We explicitly construct the analogue of the ďAlembert solution to the 1+1 wave equation in an hyperboloidal setting. This hyperboloidal ďAlembert 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.
arXiv comment21 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"
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