When black holes are merging, and emitting gravitational waves, are we seeing those waves start when the event horizons are merging, or when the singularities are merging?
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$\begingroup$ Gravitational waves are emitted by both regardless. Do you mean the "chirp" that LIGO detected in its signal? $\endgroup$– Sir CumferenceCommented Sep 8, 2016 at 14:09
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$\begingroup$ I was thinking specifically of the chirp. So gravitational waves are being emitted by any two orbiting objects? $\endgroup$– joseph.hainlineCommented Sep 8, 2016 at 14:21
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2 Answers
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The gravitational waves are actually emitted as long as you have a quadrupole moment with a second time derivative that is non-zero. The quadrupole is defined as: $$ Q_{ij}^{tt}(x) =\int\rho \left(x^i x^j - \frac{1}{3}\delta_{ij}r^2\right)\mathrm{d}^3x.$$ To simplify this, here is a rule of thumb: if you have a system that is not spherically symmetric and that is changing with time (like two black holes), you can expect gravitational waves to be emitted. For example, the system made of the Earth and the Sun is emitting ridiculously small gravitational waves (I think it is emitting a few Joules per year), but it is.
Because of how hard the waves are to measure, you can only expect to see them on Earth for black holes in their last stage, just before they merge, when the emission of gravitational waves is at its peak.
For the LIGO detection, the beginning of the signal as observed by our detectors was in the inspiral phase. This is the phase when the black holes are getting closer one to each other and losing gravitational energy (through the emission of gravitational waves), before their horizons touch. The end of the phase is actually when the black holes get within their so-called ISCO (Innermost Stable Circular Orbit), which is the smallest radius a massless particle could orbit in a stable fashion. Anything inside this orbit will slowly spiral inward and fall into the black hole.
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Gravitational waves are on peak when event horizon start merging. The black holes will merge once they are close enough. Once merged, the single hole settles down to a stable form, via a stage called ringdown and other one will be torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect". Any distortion in the shape is dissipated as more gravitational waves. In the final fraction of a second the black holes can reach extremely high velocity, and the gravitational wave amplitude reaches its peak. to know more read this https://en.wikipedia.org/wiki/Binary_black_hole#Merger
