give equations for extrinsic
data (i.e., 
-derivatives of 
that do not appear in the near-horizon geometry). On the other hand, the rest of the
Einstein equations for the near-horizon geometry restricted to the horizon vanish.- Articles
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"Classification of Near-Horizon Geometries of Extremal Black
Holes"
Hari K. Kunduri and James Lucietti
The remaining components of the Einstein equations for the full spacetime restricted to give equations for extrinsic
data (i.e., -derivatives of that do not appear in the near-horizon geometry). On the other hand, the rest of the
Einstein equations for the near-horizon geometry restricted to the horizon vanish.
give equations for extrinsic
data (i.e., -derivatives of that do not appear in the near-horizon geometry). On the other hand, the rest of the
Einstein equations for the near-horizon geometry restricted to the horizon vanish.