The ocean bulges a full meter under the Moon: that's a tide. If a massive body sits near a black hole, the hole feels a tidal pull too. In ordinary Einsteinian gravity, it doesn't respond to such a static tide: its "tidal numbers" (measures of deformability) are zero. But what if gravity is a bit more complicated?
The authors added a small cubic term to the gravitational equations — the Weyl operator cubed. It's like a spring whose Hooke's law gets an extra term with the cube of the stretch. Mathematically, the problem reduced to a system of two first-order equations. The solution showed: the correction to the hole's response is Δ(B/A) = −2400 εₑ, where εₑ is the small parameter of the addition. In the scalar equivalent, Δk₂ = −20 εₑ.
This result is not the final tidal Love number, but a convenient benchmark for comparing different calculation methods. It was obtained in metric variables and will be useful for those building a more complete theory of gravity.
Tidal Love numbers are named after the British geophysicist Augustus Love, who studied the elastic deformations of the Earth under lunar attraction.
In Alastair Reynolds's novel "Revelation Space," black holes are used as weapons, and their behavior under external influence becomes a matter of survival for civilizations.