A SCATTERING THEORY CONSTRUCTION OF DYNAMICAL VACUUM BLACK HOLES

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)633-740
Number of pages108
JournalJournal of Differential Geometry
Volume126
Issue number2
DOIs
StatePublished - Jan 2024

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint

Dive into the research topics of 'A SCATTERING THEORY CONSTRUCTION OF DYNAMICAL VACUUM BLACK HOLES'. Together they form a unique fingerprint.

Cite this