Chapter 38: Binary Mergers and Gravitational-Wave Readout

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) abbott2016observation detected the gravitational-wave signal GW150914: the merger of two black holes with masses 36 M_☉ and 29 M_☉ at a distance of ∼ 410 Mpc, releasing ∼ 3 M_☉ c² of energy in gravitational radiation over a fraction of a second. This detection confirmed a century-old prediction of general relativity and opened an entirely new observational window onto the universe.

In Category τ, gravitational waves are not ripples in a background spacetime manifold. They are boundary-character oscillations: periodic perturbations of the holonomy algebra H_∂[ω] propagating along the base τ¹ at the speed c. A binary merger is the coalescence of two coherent instances—two localized concentrations of boundary holonomy—into a single, more massive coherent instance. The gravitational-wave signal is the readout of this coalescence in the Sector D (gravity) sector.

This chapter derives the binary inspiral waveform from the τ-Einstein equation , proves the Chirp Mass Theorem

relating the waveform parameters to boundary holonomy invariants, defines the ringdown readout

as the quasi-normal mode spectrum of the merged coherent instance, and establishes the standard siren as a distance measure .