# Exact Gravitational Wave Signatures from Colliding Extreme Black Holes

## TL;DR

This paper analytically derives the gravitational wave signatures from collisions of charged black holes using a moduli space approximation, providing explicit waveforms for scattering and merging scenarios.

## Contribution

It introduces an analytical method to compute gravitational radiation from black hole collisions with arbitrary masses, extending previous approaches.

## Key findings

- Derived a simple expression for gravitational waveforms.
- Compared early and late time waveforms to theoretical expectations.
- Confirmed the quadrupolar nature of the dominant radiation.

## Abstract

The low-energy dynamics of any system admitting a continuum of static configurations is approximated by slow motion in moduli (configuration) space. Here, following Ferrell and Eardley, this moduli space approximation is utilized to study collisions of two maximally charged Reissner--Nordstr{\"o}m black holes of arbitrary masses, and to compute analytically the gravitational radiation generated by their scattering or coalescence. The motion remains slow even though the fields are strong, and the leading radiation is quadrupolar. A simple expression for the gravitational waveform is derived and compared at early and late times to expectations.