Modified Gravity Corrections in Fundamental Orbital Frequencies in Kerr Spacetime

TL;DR

This paper computes how modified gravity theories, specifically a nonlocal gravity model, cause small shifts in the fundamental orbital frequencies of objects orbiting Kerr black holes, aiding waveform modeling for gravitational wave detection.

Contribution

It introduces a perturbative method to calculate orbital frequency shifts in Kerr spacetime due to nonlocal gravity modifications, extending previous GR-based calculations.

Findings

Derived explicit formulas for frequency shifts in nonlocal gravity models.

Quantified the magnitude of frequency corrections for specific orbital parameters.

Provided a framework for incorporating modified gravity effects into gravitational waveform models.

Abstract

As a first step towards the calculation of waveform of Extreme Mass Ratio Inspirals for Modified Gravity theories, we calculate the orbital frequencies of a Small Compact Object inspiralling into a super massive blackhole for a Nonlocal gravity model. The small compact object moves along an orbit which can be approximated to a geodesic of the background spacetime due to large mass ratio of central blackhole to Small Compact Object. In General Relativity, the fundamental orbital frequencies $\Omega_r,\;\Omega_{\theta}$ and $\Omega_{\phi}$ can be calculated by solving geodesic equations of the Kerr metric. If we formulate any modified gravity theory as a small correction in General Relativity then the spacetime metric around a rotating blackhole in that theory can be considered as the Kerr metric with small deformations. This would allow us to calculate fundamental frequencies of geodetic motion of the orbiting object perturbatively i.e. as Kerr frequencies plus small shifts in Kerr frequencies coming from the modified gravity part. Using Action-angle formalism and canonical perturbation theory I calculate the frequency shifts with respect to Kerr frequencies of the orbital motion around a rotating blackhole for RR model of Nonlocal gravity theory.