ANM7 - Self Forces, Black Hole Perturbations |
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Speaker |
Rostworowski, Andrzej |
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Co-autors |
Piotr Bizon, Tadeusz Chmaj |
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Talk Title |
Non-linear effects in late-time asymptotics for self-gravitating massless fields |
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Abstract |
I will summarize recent results, obtained in collaboration with Piotr Bizon and Tadeusz Chmaj, on the non-linear origin of the power-law tails in the long-time evolution of a spherically symmetric self-gravitating massless fields in even-dimensional spacetimes. Using third-order perturbation method, we derived explicit expressions for the tail (the decay rate and the amplitude) for solutions starting from small initial data and then verified this prediction via numerical integration of the Einstein-scalar field equations. Our results show the failure of linear approximation, whose accidental success in predicting the decay rate of a spherically symmetric self-gravitating massless scalar field in $3+1$ dimensions (PRD 49, 890 (1994)) has misguided some tail hunters in the past. The talk will be based on our papers: arXiv:0812.4333, arXiv:0804.0903, arXiv:0708.1769, arXiv:math-ph/0701037 and some new unpublished results. |
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