The Lagrangian Method

• Discussion of Theory
• Status Report

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1 Black Hole

• Location of apparent horizon as determined by the residual of the apparent horizon equation using Eddington- Finkelstein coordinates. The expected plot for r=2 for M = 1 is found .
  • Residual of the apparent horizon equation
  • Case 0: Location of apparent horizon, r=2, M=1
• Location of Apparent Horizon as determined by the general apparent horizon equation in Scwarzschild coordinates.
  • Case1: A test of the general equation for 1 black hole reducing to the residual case.
  • Case2: General solution of apparent horizon location for 1 black hole.

2 Black Holes

• Location of the Apparent Horizon for two black holes at the critical separation. The critical separation for one marginally trapped surface encludes both holes for the general apparent horizon equation in Schwarzschild coordinates.
  • Case3: Location of Apparent Horizon for 2 bhs for the reduced case.
  • Case4: Location of apparent horizon for 2 black holess for the general case.