# Love in Extrema Ratio

## TL;DR

This paper reveals that in extreme-mass ratio inspirals, the tidal Love number of the central object significantly influences gravitational wave signals at leading order, enabling unprecedented tests of black hole mimickers with future detectors.

## Contribution

It uncovers a previously unnoticed effect where the tidal Love number impacts gravitational waves at leading order in the extreme-mass ratio limit, enhancing the potential to test black hole models.

## Key findings

- Extreme-mass ratio inspirals can constrain tidal Love numbers much more tightly than current methods.
- The effect magnifies the influence of the central object's tidal deformability on gravitational waves.
- Future LISA observations could probe all existing models of black hole mimickers.

## Abstract

The tidal deformability of a self-gravitating object leaves an imprint on the gravitational-wave signal of an inspiral which is paramount to measure the internal structure of the binary components. We unveil here a surprisingly unnoticed effect: in the extreme-mass ratio limit the tidal Love number of the central object (i.e. the quadrupole moment induced by the tidal field of its companion) affects the gravitational waveform at the leading order in the mass ratio. This effect acts as a magnifying glass for the tidal deformability of supermassive objects but was so far neglected, probably because the tidal Love numbers of a black hole (the most natural candidate for a compact supermassive object) are identically zero. We argue that extreme-mass ratio inspirals detectable by the future LISA mission might place constraints on the tidal Love numbers of the central object which are roughly 8 orders of magnitude more stringent than current ones on neutron stars, potentially probing all models of black hole mimickers proposed so far.