Orbital resonances in Kerr - de Sitter black holes

Abstract

The inspiral of a stellar mass compact object (1 − 100 M_⊙) into a supermassive black hole (10⁶ – 10⁹ M_⊙) in the center of galaxies are the primary generators of gravitational waves, much to the interest of current ground-based and future space-based detectors. When accurately modelled, these extreme mass ratio inspirals serve as tests for the validity of the general theory of relativity. In this paper, we determine the location of low-ordered resonances in Kerr-de Sitter black holes and study how they are affected by changes in the cosmological constant. Resonant orbits are geodesics for which the ratio of the radial and longitudinal frequencies follow the form, ω_r/ω_θ = n/m, where n,m are integers. Evolving through low-ordered resonances (small n+m value) causes jumps in the evolution of the orbital parameters which could produce phase shifts in the respective gravitational wave emission. Since typically an inspiral passes through multiple low-ordered resonances, probing the location of these resonances can help in improving current templates in gravitational wave analysis. We find that for a Kerr-de Sitter black hole (Λ > 0), the locations of the orbital resonances are shifted to larger semi-latus rectum values and lower eccentricities as the cosmological constant is increased.