Simulate a binary black hole merger and the gravitational waves it produces. See the chirp waveform h(t), the inspiral trajectory, and how LIGO detects the spacetime strain.
Gravitational wave frequency during inspiral: f(τ) ∝ (GM_chirp/c³)^(−5/8) · τ^(−3/8), where τ is time to merger. Chirp mass M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5). Strain h(t) ∝ (πf)^(2/3)·cos(2πft). Merger frequency at ISCO: f_ISCO = c³/(6^(3/2)·π·GM_total).
LIGO measures the strain h = ΔL/L — the fractional change in arm length caused by passing gravitational waves. For GW150914, h_peak ≈ 10⁻²¹, meaning the 4 km arms changed by ~10⁻¹⁸ m — smaller than a proton. LIGO must distinguish this from seismic noise, thermal fluctuations, and quantum shot noise.
As two black holes spiral inward, they lose energy to gravitational radiation, so they orbit faster and closer. This produces the characteristic "chirp": increasing frequency and amplitude culminating in the merger. The chirp mass can be extracted from the frequency evolution with extremely high precision — LIGO's most sensitive measurement.