3-D Snapshots of Apparent Horizons in MCF Tracking Method: Searching for the Breaking Point

Snapshots of the surface, in cartesian coordinates, are shown below for a two black hole system.

Grid size: 17

Masses: 0.5M each

Separation: 0.0M

Single, spherical horizon is found with a curvature over the surface of 10^-8 and a radius of 1.0M.

Grid size: 17

Masses: 1.0M each

Separation: 0.0M

Single, spherical apparent horizon is found with a constant curvature at 10^-8 and a raduis of 2.0M.

Grid size: 17

Masses: 1.0M each

Separation: 3.1M

Single, spherical apparent horizon is found with a curvature of 10^-8.  This separation is near the critical separation beyond which there is no single apparent horizon enveloping both masses.