Paper
Improved decay for quasilinear wave equations close to asymptotically flat spacetimes including black hole spacetimes
Authors
Shi-Zhuo Looi
Abstract
We study the quasilinear wave equation where the metric is close to and asymptotically approaches , which equals the Schwarzschild metric or a Kerr metric with small angular momentum, as time tends to infinity. Under only weak assumptions on the metric coefficients, we prove an improved pointwise decay rate for the solution . One consequence of this rate is that for bounded , we have the integrable decay rate where is a parameter governing the decay, near the light cone, of the coefficient of the slowest-decaying term in the quasilinearity. We also obtain the same aforementioned pointwise decay rates for the quasilinear wave equation with a more general asymptotically flat metric and with other time-dependent asymptotically flat lower order terms.