A figure skater spins on the ice, gradually spiraling inward. Similarly, a small star or black hole orbiting a massive black hole loses energy. It emits gravitational waves — ripples in spacetime that detectors on Earth pick up.
But the dance of this pair is more intricate than it seems. The small companion isn't just a point. It has its own rotation (like a spinning top) and a shape that deforms under the giant's tidal forces. These details affect how quickly energy is lost, and thus the very signal we hear. For the first time, the authors have calculated these effects with full precision, using Einstein's theory of relativity Einstein and the 'self-force' method.
The results are not just mountains of precise numbers but also handy formulas that other scientists can use. They will improve models of gravitational-wave signals for any unequal pair — from a star and a black hole to two black holes of different masses. This means future detectors like the Einstein Telescope or LISA will be able to catch even the faintest 'notes' of the cosmic orchestra.
So the dance of a tiny star around a black hole becomes a key to understanding how gravity works in the most extreme conditions. And each new, more precise calculation brings us closer to hearing this music of the spheres in all its fullness.
Gravitational waves from black hole mergers were first detected in 2015, but their existence was predicted by Einstein as early as 1916.
In the movie "Interstellar," a planet is shown orbiting a supermassive black hole — systems like this are exactly what this study examines.