Gravitational self-force corrections to tidal invariants for particles on eccentric orbits in a Schwarzschild spacetime

TL;DR

This paper calculates first-order gravitational self-force corrections to tidal invariants for particles on eccentric orbits in Schwarzschild spacetime, extending previous circular orbit results to include eccentricity effects up to high post-Newtonian order.

Contribution

It provides the first-order conservative self-force corrections to tidal eigenvalues for eccentric orbits, generalizing prior circular orbit analyses.

Findings

Corrections computed up to 9.5 post-Newtonian order.

Results include eccentricity effects up to second order.

Previous circular orbit results are recovered in the limit.

Abstract

We study tidal effects induced by a particle moving along a slightly eccentric equatorial orbits in a Schwarzschild spacetime within the gravitational self-force framework. We compute the first order (conservative) corrections in the mass-ratio to the eigenvalues of the electric-type and magnetic-type tidal tensors up to the second order in eccentricity and through the 9.5 post-Newtonian order. Previous results on circular orbits are thus generalized and recovered in a proper limit.