ausblenden:
Schlagwörter:
General Relativity and Quantum Cosmology, gr-qc
Zusammenfassung:
From numerical simulations of the Einstein equations, and also from
gravitational wave observations, the gravitational wave signal from a binary
black hole merger is seen to be simple and to possess certain universal
features. The simplicity is somewhat surprising given that non-linearities of
general relativity are thought to play an important role at the merger. The
universal features include an increasing amplitude as we approach the merger,
where transition from an oscillatory to a damped regime occurs in a pattern
apparently oblivious to the initial conditions. We propose an Airy-function
pattern to model the binary black hole (BBH) merger waveform, focusing on
accounting for its simplicity and universality. We postulate that the relevant
universal features are controlled by a physical mechanism involving: i) a
caustic phenomenon in a basic `geometric optics' approximation and, ii) a
diffraction over the caustic regularizing its divergence. Universality of
caustics and their diffraction patterns account for the observed universal
features, as in optical phenomena such as rainbows. This postulate, if true,
allows us to borrow mathematical techniques from Singularity (Catastrophe)
Theory, in particular Arnol'd-Thom's theorem, and to understand binary mergers
in terms of fold caustics. The diffraction pattern corresponding to the
fold-caustic is given in terms of the Airy function, which leads (under a
`uniform approximation') to the waveform model written in terms of a
parameterized Airy function. The post-merger phase does not share the same
features of simplicity and universality, and must be added separately.
Nevertheless, our proposal allows a smooth matching of the inspiral and
post-merger signals by using the known asymptotics of the Airy function.
