Gravitational waves — merging black holes (LIGO)

What just happened?

Two black holes orbit a common centre and radiate energy as gravitational waves — ripples in spacetime itself. As they lose energy, the orbit tightens, the revolution speeds up, and the wave grows in frequency and amplitude until the merger (chirp). Then the resulting remnant "rings" and the oscillation decays away (ringdown).

Chirp mass — the parameter that drives the signal:

It determines how fast the chirp builds and how strong the signal is. The wave frequency in the inspiral phase grows as $f_{\text{GW}}(t)\propto (t_{\text{merge}}-t)^{-3/8}$, and the received amplitude falls off with distance: $h\propto \mathcal{M}_c^{5/3}/D$.

Invariant — the energy balance:

The energy carried away by the waves is exactly the loss of the system's orbital energy. That is why the orbit cannot stay constant — it must tighten, and that inevitably drives the frequency up. Hence the characteristic chirp just before the merger.

LIGO detection:

The first direct measurement of a gravitational wave (GW150914) came in 2015 — the merger of two black holes of about 36 and 29 solar masses, over a billion light-years away. Nobel Prize 2017. The interferometer measures changes in arm length smaller than a thousandth of a proton's diameter. It is a new "window" onto the Universe — we observe objects invisible in any light.

Why this matters for your exam:

It is a spectacular extension of the waves topic — it shows live that a wave has frequency, amplitude and speed (gravitational waves travel at the speed of light), and that these properties can change over time. It links the waves unit with gravity and black-hole physics — a favourite context for "real-life" problems and questions about modern physics.

Remember: the system loses energy to the waves → the orbit tightens → the frequency rises sharply (chirp) until the merger. $f_{\text{GW}}\propto (t_{\text{merge}}-t)^{-3/8}$.