BHBH with spin

  1. Introduction
  2. Binary Inspiral and Merger
  3. Final Black Hole Parameters


Fig. 1-1 Initial Configuration of Binary
Fig. 1-1 Initial Configuration of Binary
Evolution is performed with the BSSN scheme on an AMR grid with 10 levels of refinement. The mesh spacing ranges from ΔXmax = 12.1 M in the outermost level to ΔXmin = 0.024 M in the innermost level. In this simulation, the initial coordinate radius of the binary orbit is D0/M = 9.89. Here M is the total initial binary ADM mass. The black hole interiors, bounded by their apparent horizons, are denoted by black spheres. Their motion is shown in the orbital plane. The evolution is performed with "moving puncture" gauge conditions. (Note: The circle in the lower right-hand corner of the above figure is a clock.)

Binary Inspiral and Merger

The binary makes approximately six orbits prior to merging at t ≈ 1400 M. As the inital binary merges, we see the development of a common horizon which oscillates until settling down at t ≈ 1450 M. The simulation continues until t = 1590 M to demonstrate the stability of the resulting Kerr black hole. The early growth of the apparent horizons is a gauge (coordinate) effect.
Evolution at t/M = 0
Fig. 2-1 Evolution at t/M = 0
Fig. 2-2 Evolution at t/M = 400
Fig. 2-2 Evolution at t/M = 400
Fig. 2-3 Evolution at t/M = 1450
Fig. 2-3 Evolution at t/M = 1450
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Final Black Hole Parameters

Listed in the table below is the dimensionless spin of the black hole at the end of our simulation. Also shown are the radiated energy and angular momentum from gravitational wave emission. Here, M is the initial ADM mass whereas MBH is the final ADM mass of the black hole.
MBH/M 0.91
JBH/MBH2 0.92
ΔE GW/M 8.5%
ΔJGW/M2 59%
δE ≡ (M-MBH-ΔEGW)/M -2.2 x 10-3
δJ ≡ (J-JBH-ΔJGW)/M 6 x 10-4
Our simulation maintains excellent conservation of energy and momentum, since δE and δJ are on the order of 10-3 and 10-4, respectively.