# Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system

## TL;DR

This paper studies how the spin of a test body and the cosmological constant influence the orbital deviation and gravitational wave phase shift in extreme mass ratio inspiral systems, highlighting the dominant effects of spin near the black hole and the significance of the cosmological constant at larger distances.

## Contribution

It provides a detailed analysis of the combined effects of particle spin and cosmological constant on orbital deviations in EMRI systems, which was not thoroughly explored before.

## Key findings

- Spin-induced deviations are larger than those from the cosmological constant near the black hole.
- The phase shift from the cosmological constant becomes significant at large distances.
- Phase shift accumulation from the cosmological constant can be ignored close to the black hole.

## Abstract

The future space-borne detectors will provide the possibility to detect gravitational waves emitted from extreme mass ratio inspirals of stellar-mass compact objects into supermassive black holes. It is natural to expect that the spin of the compact object and cosmological constant will affect the orbit of the inspiral process and hence lead to the considerable phase shift of the corresponding gravitational waves. In this paper, we investigate the motion of a spinning test particle in the spinning black hole background with a cosmological constant and give the order of motion deviation induced by the particle's spin and the cosmological constant by considering the corresponding innermost stable circular orbit. By taking the neutron star or kerr black hole as the small body, the deviations of the innermost stable circular orbit parameters induced by the particle's spin and cosmological constant are given. Our results show that the deviation induced by particle's spin is much larger than that induced by cosmological constant when the test particle locates not very far away from the black hole, the accumulation of phase shift during the inspiral from the cosmological constant can be ignored when compared to the one induced by the particle's spin. However when the test particle locates very far away from the black hole, the impact from the cosmological constant will increase dramatically. Therefore the accumulation of phase shift for the whole process of inspiral induced by the cosmological constant and the particle's spin should be handled with caution.