Periodic orbits and gravitational waveforms of spinning particles in nonlocal Gravity

TL;DR

This study explores how nonlocal gravity influences the orbits and gravitational wave signals of spinning particles around black holes, revealing observable differences from classical predictions that could test gravity theories.

Contribution

It introduces a detailed analysis of spinning particle dynamics and gravitational waveforms in nonlocal gravity, highlighting effects of nonlocal parameters on orbital stability and wave phase.

Findings

Nonlocal parameters significantly affect effective potential and innermost stable orbit.

Gravitational wave phase shifts depend on nonlocal parameters, with delays and advances observed.

Waveform mismatches suggest potential for observational tests of nonlocal gravity.

Abstract

In this paper, we investigate the dynamics and gravitational-wave signatures of periodic orbits of spinning test particles moving in the equatorial plane around static, spherically symmetric black holes within the framework of Deser-Woodard nonlocal gravity. Based on the Mathisson-Papapetrou-Dixon equations, combined with the Tulczyjew spin supplementary condition, we derive the orbital dynamic equations for spinning particles moving in the equatorial plane and impose a timelike constraint to exclude unphysical superluminal trajectories. By comparing with the classical Schwarzschild black hole, we systematically analyze the effects of the nonlocal gravitational parameters $\zeta$ and $b$ on the effective potential governing the radial motion of particles and the innermost stable circular orbit. In addition, gravitational waveforms exhibit significant phase differences: an increase in $\zeta$ induces a phase delay, whereas an increase in $b$ results in a phase advance. A one-year simulation of the orbital evolution of an extreme mass ratio inspiral demonstrates that when $b=2$ and $\zeta\approx10^{-6}$, the mismatch between the gravitational waveforms predicted for the nonlocal gravity black hole and those for the Schwarzschild black hole reaches the distinguishable threshold ($\mathcal{M}=0.0125$), providing a basis for observational discrimination between general relativity and nonlocal gravity.