# Relativistic Effects in Extreme Mass Ratio Gravitational Wave Bursts

## TL;DR

This paper examines how relativistic effects influence gravitational wave signals from extreme mass ratio bursts, highlighting their significance for detection and black hole spin measurement.

## Contribution

It introduces a geodesic-based relativistic model for EMRBs and assesses the impact of relativistic corrections on waveform accuracy and parameter estimation.

## Key findings

- Relativistic EMRBs are common, constituting about half of the events.
- Relativistic corrections significantly alter waveform amplitude and phase.
- Dephasing could help measure black hole spin and test relativistic gravity.

## Abstract

Extreme mass ratio bursts (EMRBs) have been proposed as a possible source for future space-borne gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). These events are characterized by long-period, nearly-radial orbits of compact objects around a central massive black hole. The gravitational radiation emitted during such events consists of a short burst, corresponding to periapse passage, followed by a longer, silent interval. In this paper we investigate the impact of including relativistic corrections to the description of the compact object's trajectory via a geodesic treatment, as well as including higher-order multipole corrections in the waveform calculation. The degree to which the relativistic corrections are important depends on the EMRB's orbital parameters. We find that relativistic EMRBs (v_{max}}/c > 0.25) are not rare and actually account for approximately half of the events in our astrophysical model. The relativistic corrections tend to significantly change the waveform amplitude and phase relative to a Newtonian description, although some of this dephasing could be mimicked by parameter errors. The dephasing over several bursts could be of particular importance not only to gravitational wave detection, but also to parameter estimation, since it is highly correlated to the spin of the massive black hole. Consequently, we postulate that if a relativistic EMRB is detected, such dephasing might be used to probe the relativistic character of the massive black hole and obtain information about its spin.