Self-force corrections to the periapsis advance around a spinning black hole

TL;DR

This paper presents high-precision calculations of self-force corrections to periapsis advance around spinning black holes, providing benchmarks, discriminating between theoretical models, and exploring the ISCO shift in near-extremal regimes.

Contribution

It introduces the first high-precision calculation of linear mass ratio corrections to periapsis advance for spinning black holes and extends the understanding of ISCO shifts into near-extremal spins.

Findings

High-precision correction calculations serve as benchmarks for models.

Discriminates between two incompatible 4PN equations of motion.

Reveals oscillatory behavior of ISCO shift near extremal spins.

Abstract

The linear in mass ratio correction to the periapsis advance of equatorial orbits around a spinning black hole is calculated for the first time and to very high precision, providing a key benchmark for different approaches modelling spinning binaries. The high precision of the calculation is leveraged to discriminate between two recent incompatible derivations of the 4PN equations of motion. Finally, the limit of the periapsis advance near the innermost stable orbit (ISCO) allows determination of the ISCO shift, validating previous calculations using the first law of binary mechanics. Calculation of the ISCO shift is further extended into the near extremal regime (with spins up to $1-a=10^{-20}$), revealing new unexpected phenomenology. In particular, we find that the shift of the ISCO does not have a well defined extremal limit, but instead continues to oscillate.