| Title: |
Optimal decay for solutions of the Teukolsky equation on the Kerr metric for the full subextremal range |a| < M ; Décroissance optimale pour les solutions de l'équation de Teukolsky sur la métrique de Kerr pour tout l'intervalle sous-extremal $\lvert a\rvert |
| Authors: |
Millet, Pascal |
| Contributors: |
Université Grenoble Alpes (UGA) |
| Source: |
https://hal.science/hal-03987465 ; 2023. |
| Publisher Information: |
HAL CCSD |
| Publication Year: |
2023 |
| Collection: |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
| Subject Terms: |
Teukolsky equation; Kerr black hole; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]; [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] |
| Description: |
We derive the large time asymptotics of initially regular and localized solutions of the Teukolsky equation on the exterior of a subextremal Kerr black hole for any half integer spin. More precisely, we obtain the leading order term (predicted by Price's law) in the large time regime assuming that the initial data have compact support and have enough (but finite) Sobolev regularity. For initial data with less spatial decay (typically decaying like r^{−1−α} with α ∈ (0, 1)), we prove that the solution has a pointwise decay of order t^{−1−α−s−|s|+} on spatially compact regions. In the proof, we adopt the spectral point of view and make use of recent advances in microlocal analysis and non elliptic Fredholm theory which provide a robust framework to study linear operators on black hole type spacetimes. |
| Document Type: |
report |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/2302.06946; hal-03987465; https://hal.science/hal-03987465; https://hal.science/hal-03987465/document; https://hal.science/hal-03987465/file/decayTeukolsky5.pdf; ARXIV: 2302.06946 |
| Availability: |
https://hal.science/hal-03987465; https://hal.science/hal-03987465/document; https://hal.science/hal-03987465/file/decayTeukolsky5.pdf |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.F3246117 |
| Database: |
BASE |