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 -