The r^p-weighted energy method of Dafermos and Rodnianski in general asymptotically flat spacetimes and applications

2015/09/28 by Moschidis, Georgios
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1509.08489

Abstract

In [M. Dafermos and I. Rodnianski, A new physical-space approach to decay for the wave equation with applications to black hole spacetimes, in XVIth International Congress on Mathematical Physics, Pavel Exner ed., Prague 2009 pp. 421-433, 2009, arXiv:0910.4957], Dafermos and Rodnianski presented a novel approach to establish uniform decay rates for solutions ϕ to the scalar wave equation \square_gϕ=0 on Minkowski, Schwarzschild and other asymptotically flat backgrounds. This paper generalises the methods and results of the above paper to a broad class of asymptotically flat spacetimes (M,g), including Kerr spacetimes in the full subextremal range |a|

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