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We consider in this work the asymptotics of a Maxwell field in Schwarzschildand Kerr spacetimes. In any subextremal Kerr spacetime, we show energy andpointwise decay estimates for all components under an assumption of a basicenergy and Morawetz estimate for spin $\pm 1$ components. If restricted toslowly rotating Kerr, we utilize the basic energy and Morawetz estimates provenin an earlier work to further improve these decay estimates such that the totalpower 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 almostsharp 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 fieldtowards a static solution on a Schwarzschild background. All estimates areuniform in the exterior of the black hole.

Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field