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Hyperboloidal
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The slides from my talk at Benasque during the "Frontiers in strong gravity" meeting (https://www.benasque.org/2022relativity/cgi-bin/talks/allprint.pl): https://www.benasque.org/2022relativity/talks_contr/083_alex_vano-vinuales.pdf
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A website on hyperboloidal work that we are setting up (still under construction): https://hyperboloid.al/ There will be some tutorials and simpler explanations.
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To start I would recommend this paper by Anil Zenginoglu: https://arxiv.org/abs/0712.4333 Some work evolving the wave equation on a Kerr hyperboloidal background with the Einstein Toolkit (and another pseudospectral code) is: https://arxiv.org/abs/1109.2513 Maybe chapter 2 in Anil Zenginoglu's PhD thesis: https://arxiv.org/abs/0711.0873 Perhaps Alex Vano-Vinuales' PhD thesis: https://arxiv.org/abs/1512.00776