Decay of solutions of the wave equation in cosmological spacetimes -- a numerical analysis
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911450421788672 |
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| author | Rossetti, Flavio Vañó-Viñuales, Alex |
| author_facet | Rossetti, Flavio Vañó-Viñuales, Alex |
| contents | We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative relation between the expansion rate of the underlying background universe and the decay rate of linear waves, also in the context of spatially-hyperbolic spacetimes, for which rigorous proofs of decay rates are not generally known. A prominent role in the decay mechanism is shown to be played by tails, i.e. scattered waves propagating in the interior of the lightcone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06666 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decay of solutions of the wave equation in cosmological spacetimes -- a numerical analysis Rossetti, Flavio Vañó-Viñuales, Alex General Relativity and Quantum Cosmology We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative relation between the expansion rate of the underlying background universe and the decay rate of linear waves, also in the context of spatially-hyperbolic spacetimes, for which rigorous proofs of decay rates are not generally known. A prominent role in the decay mechanism is shown to be played by tails, i.e. scattered waves propagating in the interior of the lightcone. |
| title | Decay of solutions of the wave equation in cosmological spacetimes -- a numerical analysis |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2302.06666 |