Gravitational self-force corrections to tidal invariants for particles on circular orbits in a Kerr spacetime

TL;DR

This paper extends self-force calculations of tidal invariants from Schwarzschild to Kerr spacetimes, providing analytical corrections for particles on circular orbits, which enhances understanding of gravitational effects in rotating black hole environments.

Contribution

It introduces the first self-force corrections to tidal invariants in Kerr spacetime, including eigenvalues of tidal tensors, up to high post-Newtonian orders.

Findings

Derived linear-in-mass-ratio corrections for electric and magnetic tidal invariants.

Computed eigenvalues of tidal tensors analytically through high post-Newtonian orders.

Extended previous Schwarzschild results to rotating Kerr black holes.

Abstract

We generalize to the Kerr spacetime existing self-force results on tidal invariants for particles moving along circular orbits around a Schwarzschild black hole. We obtain linear-in-mass-ratio corrections to the quadratic and cubic electric-type invariants and the quadratic magnetic-type invariant in series of the rotation parameter up to the fourth order. We then construct the eigenvalues of both electric and magnetic tidal tensors and analytically compute them through high post-Newtonian orders.