# Gravitational Waveforms

The gravitational wavetrain from a compact binary system may be separated into three qualitatively different phases: the inspiral, merger, and ringdown. During the inspiral phase, which takes up most of the binary's lifetime, gravity wave emission gradually reduces the binary separation. When the black holes get close enough, they merge into one black hole. Finally, ringdown radiation is emitted as the distorted black hole settles down to Kerr-like equilibrium (Note: Only in the case of a vacuum spacetime does the spinning BH obey the exact Kerr solution. The BHs formed here are surrounded by gaseous disks with small, but nonnegligible, rest mass). Both polarization modes (h+ and hx) are shown.

## Case 1: q = 1:1

In the post-decoupling regime, we have two black holes with equal mass inspiraling towards each other surrounded by a gaseous disk. Shown below are hx and h+ in just the lower hemisphere. Waveforms are plotted in the region of r/M ≥ 60. The evolution is followed through inspiral, merger, and ringdown. The matter is now evolved by solving the relativistic MHD equations and the gravitational field is evolved by solving the Einstein field equations via the BSSN formalism.

### Case 1: q = 1:1 - hx Polarization (Lower Hemisphere)

 Fig. 3-1: hx at time t/M = 227 Fig. 3-2: hx at time t/M = 536 Fig. 3-3: hx at time t/M = 947 Fig. 3-4: hx at time t/M = 1037 Fig. 3-5: hx at time t/M = 1070 Fig. 3-6: hx at time t/M = 1103
Play Case 1: q = 1:1 - hx (Lower Hemisphere)

### Case 1: q = 1:1 - h+ Polarization (Lower Hemisphere)

 Fig. 3-1: h+ at time t/M = 227 Fig. 3-2: h+ at time t/M = 536 Fig. 3-3: h+ at time t/M = 947 Fig. 3-4: h+ at time t/M = 1037 Fig. 3-5: h+ at time t/M = 1070 Fig. 3-6: h+ at time t/M = 1103
Play case 1: q = 1:1 - h+ (Lower Hemisphere)