Relativistic orbits and Gravitational Waves from gravitomagnetic corrections

TL;DR

This paper explores higher-order gravitomagnetic corrections to relativistic orbits, revealing a new nutation effect and analyzing its impact on gravitational waveforms from compact objects captured by massive black holes, relevant for future GW detection.

Contribution

It introduces a new nutation effect due to gravitomagnetic corrections and studies its influence on gravitational waveforms emitted during black hole captures.

Findings

Discovery of a new nutation effect from gravitomagnetic corrections.

Numerical estimates of gravitational wave amplitudes affected by these corrections.

Potential relevance for future space-based gravitational wave detectors like LISA.

Abstract

Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the ${\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.