TY - JOUR

T1 - A SCATTERING THEORY CONSTRUCTION OF DYNAMICAL VACUUM BLACK HOLES

AU - Dafermos, Mihalis

AU - Holzegel, Gustav

AU - Rodnianski, Igor

N1 - Publisher Copyright:
© 2024 International Press, Inc.. All rights reserved.

PY - 2024/1

Y1 - 2024/1

N2 - 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.

AB - 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.

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U2 - 10.4310/jdg/1712344221

DO - 10.4310/jdg/1712344221

M3 - Article

AN - SCOPUS:85189771007

SN - 0022-040X

VL - 126

SP - 633

EP - 740

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 2

ER -