Almost sharp asymptotics for Maxwell field on black hole spacetimes

2020.06.30（星期二），14:00-15:00

點：騰訊會議

要：We consider the asymptotics of a Maxwell field in the exterior of a Schwarzschild or Kerr black hole. In a subextremal Kerr spacetime, we show all components are asymptotic to a stationary solution under an assumption of a basic energy and Morawetz estimate for spin $\pm 1$ components, and prove the total power of decay is $-7/2$. On a Schwarzschild spacetime, we construct a conserved Newman--Penrose constant for any $\ell$ mode, and depending on if this constant vanishes or not, we prove almost sharp Price's law decay $\tau^{-5+}$ (or $\tau^{-4+}$) for Maxwell field and $\tau^{-\ell -4+}$ (or $\tau^{-\ell -3+}$) for any $\ell$ mode of the field towards a static solution on a Schwarzschild background.

https://meeting.tencent.com/s/r7bGZcsDfgzQ