love number

The ocean bulges toward the Moon in a tidal hump. But some objects do the opposite — instead of stretching matter, the tide presses a dent into it. These are boson stars: invisible clumps of boson particles that can all collapse into a single quantum state. Normal matter is propped up by heat; boson stars are held together by quantum pressure.

Two neutron stars whirl in a close dance, each feeling the tidal field of its partner. It's like the Moon raising oceans on Earth, but here it's spacetime itself and the star's matter that deform. Astrophysicists call this tidal deformation — a measure of how much an object 'bends' under the gravitational pull of its companion.

A black hole is not a deaf wall. Give it a gentle tap, and it will respond. Physicists call this 'tidal deformability'—an object's ability to change shape under an external force. For a static black hole, this ability is zero: a static field doesn't bend it.

When two neutron stars circle each other, they don't remain rigid spheres. The partner's gravity stretches each star, creating tidal bulges — much like the Moon raises ocean tides on Earth. But unlike water, here it's superdense matter that deforms: a teaspoon of this stuff weighs billions of tons.

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.

Drop a pebble into a pond — ripples spread across the water. In much the same way, a massive body circling a black hole perturbs the fabric of spacetime, generating gravitational waves. But what if the pond itself isn't flat, but has hidden folds — extra dimensions invisible to the eye?

A stone falls into a pond, and ripples spread across the water. Similarly, a black hole resting in the void may encounter a gravitational wave or a cloud of gas. It does not remain indifferent: its surface (the event horizon) bends slightly, like a stretched membrane under the weight of a drop.

If two steel balls circle each other, their mutual attraction is powerless to change each other's shape. A water ball, on the contrary, would stretch out like a droplet.

In general relativity, a black hole has long been regarded as a perfect mirror: no matter what fields fall onto it, it does not deform. The tidal Love numbers, which measure how a body deforms under an external tidal field, turned out to be zero for scalar, electromagnetic, and gravitational perturbations.