6: The Inner Boundary (cont.)

• The Schwarzschild (Ingoing Eddington-Finklestein) and Kerr spacetimes use the Kerr-Schild form of the metric:

• • The metric is form invariant under a boost.
  • The 3+1 decomposition are unique for boosted Schwarzschild or Kerr.
  • 3+1 decomposition gives us initial data (gij, Kij) and coordinate conditions (a,bi) which we can then use.
  • The analytical apparent horizon location is known everywhere.

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