# Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations

## TL;DR

This paper discusses how exact solutions of Einstein's equations and particle motion can set constraints on gravitational wave phenomena near black holes, with implications for waveform modeling in binary mergers.

## Contribution

It introduces a method combining Einstein solutions and particle dynamics to analyze gravitational wave emissions in Schwarzschild and Kerr geometries.

## Key findings

- Different initial conditions lead to distinct gravitational wave signatures.
- The approach helps distinguish burst-like signals from smooth mergers.
- Constraints on possible gravitational wave phenomena are established.

## Abstract

We show how the concurrent implementation of the exact solutions of the Einstein equations, of the equations of motion of the test particles, and of the relativistic estimate of the emission of gravitational waves from test particles, can establish a priori constraints on the possible phenomena occurring in Nature. Two examples of test particles starting at infinite distance or from finite distance in a circular orbit around a Kerr black hole are considered: the first leads to a well defined gravitational wave burst the second to a smooth merging into the black hole. This analysis is necessary for the study of the waveforms in merging binary systems.