Eur. Phys. J. C (2019) 79: 856
https://doi.org/10.1140/epjc/s10052-019-7334-y

Regular Article - Theoretical Physics

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

¹ Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou, 730000, China
² Key Laboratory for Magnetism and Magnetic of the Ministry of Education, Lanzhou University, Lanzhou, 730000, China
³ Institute of Space Sciences (ICE, CSIC) and Institut d’Estudis Espacials de Catalunya (IEEC) at Campus UAB, Carrer de Can Magrans s/n, 08193, Barcelona, Spain
⁴ Institute of Applied Mathematics, Academy of Mathematics and Systems Science, CAS, Beijing, 100190, China
⁵ Kavli Institute for Astronomy and Astrophysics, Beijing, 100871, China

^* e-mail: liuyx@lzu.edu.cn

Received: 31 May 2019
Accepted: 21 September 2019
Published online: 17 October 2019

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.