3:ADM 3+1 form (cont.)

• The extrinsic curvature is a spacelike object which determines the contraction and shear of the normals to the hypersurface.

• We can rewrite the ADM equations as:

  ¶t gij = Lb gij - 2 a Kij
  
  ¶t Kij = Lb Kij - Di Dj a + a(Rij + K Kij -2Kli Klj
  • where Lb Kij = bk ¶kKij + Kkj ¶i bk + Kik ¶jbk

• Causal Differencing:

  • Before we describe causal differencing, a key ingredient for the evolution of black holes, we must state the desired properties of a black hole evolution scheme.

Previous slide

Next slide

Back to first slide

View graphic version