1. The three phases of coalescence
The evolution of a binary black hole system falls into three stages:
inspiral (the pair gradually spirals together as it loses energy to gravitational waves),
merger — the plunge past the innermost stable circular orbit (RISCO) at speeds of up to 0.6c and the merging of the event horizons, and
ringdown — the damped quasinormal-mode (QNM) oscillations of the newborn rotating Kerr black hole.
r(t) ∝ (t_c − t)^(1/4), f_GW(t) ∝ (t_c − t)^(−3/8)
2. Gravitational lensing and the photon sphere
Near the event horizon (Rs = 2GM/c²), photons from distant stars and nebulae are deflected by the curved spacetime metric. At the radius rph = 1.5 Rs light can orbit the black hole, forming a bright photon ring and secondary Einstein rings.
d²x/ds² = − (3/2) R_s · |r × d|² / r⁵ · r
3. Quadrupole gravitational waves (h₊ and hₓ)
A rapidly orbiting pair of massive bodies generates ripples in the spacetime metric that travel at the speed of light in the shape of an Archimedean spiral. At the peak of the GW150914 merger an energy of 3.0 M☉c² was released within a fraction of a second — the peak radiated power exceeded the combined luminosity of all the stars in the visible Universe.
𝓜_c = (M₁ M₂)^(3/5) / (M₁ + M₂)^(1/5)
4. Relativistic Doppler effect and frame dragging
The accretion-disk plasma orbits at nearly the speed of light. Because of relativistic beaming (I ∝ D3+α), the side of the disk approaching us looks many times brighter and shifts toward the blue end of the spectrum, while the receding side dims and turns red. The spin of the holes themselves (χ1,2) twists the space around them (the Lense–Thirring effect).
D = 1 / [γ · (1 − (v/c) cos θ)]