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Price’s Law and Precise Late-Time Asymptotics for Subextremal Reissner–Nordström Black Holes

2023; Birkhäuser; Volume: 24; Issue: 9 Linguagem: Inglês

10.1007/s00023-023-01328-8

1424-0661

Yannis Angelopoulos, Stefanos Aretakis, Dejan Gajic,

Cosmology and Gravitation Theories

In this paper, we prove precise late-time asymptotics for solutions to the wave equation supported on angular frequencies greater or equal to $\ell$ on the domain of outer communications of subextremal Reissner-Nordstr\"om spacetimes up to and including the event horizon. Our asymptotics yield, in particular, sharp upper and lower decay rates which are consistent with Price's law on such backgrounds. We present a theory for inverting the time operator and derive an explicit representation of the leading-order asymptotic coefficient in terms of the Newman-Penrose charges at null infinity associated with the time integrals. Our method is based on purely physical space techniques. For each angular frequency $\ell$ we establish a sharp hierarchy of $r$-weighted radially commuted estimates with length $2\ell+5$. We complement this hierarchy with a novel hierarchy of weighted elliptic estimates of length $\ell+1$.