A scattering theory construction of dynamical vacuum black holes

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Title: A scattering theory construction of dynamical vacuum black holes
Author(s): Holzegel, G
Dafermos, M
Rodnianski, I
Item Type: Journal Article
Abstract: We construct a large class of dynamical vacuum black hole spacetimes whose exterior geometry asymptotically settles down to a fixed Schwarzschild or Kerr metric. The construction proceeds by solving a backwards scattering problem for the Einstein vacuum equations with characteristic data prescribed on the event horizon and (in the limit) at null infinity. The class admits the full “functional” degrees of freedom for the vacuum equations, and thus our solutions will in general possess no geometric or algebraic symmetries. It is essential, however, for the construction that the scattering data (and the resulting solution spacetime) converge to stationarity exponentially fast, in advanced and retarded time, their rate of decay intimately related to the surface gravity of the event horizon. This can be traced back to the celebrated redshift effect, which in the context of backwards evolution is seen as a blueshift.
Date of Acceptance: 16-Dec-2014
URI: http://hdl.handle.net/10044/1/29517
ISSN: 1945-743X
Publisher: International Press
Journal / Book Title: Journal of Differential Geometry
Copyright Statement: This article is under embargo until publication
Keywords: 0101 Pure Mathematics
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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