论文标题
Schwarzschild的几乎价格定律和Kerr的Maxwell Field的衰减估算值
Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
论文作者
论文摘要
我们在这项工作中考虑了Schwarzschild和Kerr SpaceTimes的Maxwell Field的渐近学。在任何次级Kerr时空中，我们在假设基本能量和Morawetz估算的旋转$ \ pm 1 $组件的假设下显示了所有组件的能量和衰减估计值。如果仅限于缓慢旋转的Kerr，我们利用基本能量和摩拉维兹的估计值在较早的工作中得到证明，以进一步改善这些衰减估计值，以便麦克斯韦球场所有成分的衰减总功率为$ -7/2 $ $ -7/2 $。最后，取决于纽曼（newman）是否不断消失，我们证明了麦克斯韦（Maxwell Field）的几乎急剧定律的定律衰减$τ^{ - 5+} $（或$τ^{ - 4+} $），$τ^{ - \ ell -4+} $（或$ f.ell -4+} $（或$ f. el $ f. Schwarzschild背景。所有估计在黑洞的外部均均匀。
We consider in this work the asymptotics of a Maxwell field in Schwarzschild and Kerr spacetimes. In any subextremal Kerr spacetime, we show energy and pointwise decay estimates for all components under an assumption of a basic energy and Morawetz estimate for spin $\pm 1$ components. If restricted to slowly rotating Kerr, we utilize the basic energy and Morawetz estimates proven in an earlier work to further improve these decay estimates such that the total power of decay for all components of Maxwell field is $-7/2$. In the end, depending on if the Newman--Penrose constant vanishes or not, we prove almost sharp Price's law decay $τ^{-5+}$ (or $τ^{-4+}$) for Maxwell field and $τ^{-\ell -4+}$ (or $τ^{-\ell -3+}$) for any $\ell$ mode of the field towards a static solution on a Schwarzschild background. All estimates are uniform in the exterior of the black hole.
