Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591946 | Journal of Functional Analysis | 2009 | 90 Pages |
Abstract
The Schwarzschild and Reissner–Nordstrøm solutions to Einstein's equations describe space–times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space–time of this type. We show that for solutions with initial data which decay at infinity and at the bifurcation sphere, a weighted L6 norm in space decays like . This weight vanishes at the event horizon, but not at infinity. To obtain this control, we require only an ϵ loss of angular derivatives.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory