Scalar field self-force effects on orbits about a Schwarzschild black hole

TL;DR

This paper calculates how a scalar field self-force affects the motion of particles around a Schwarzschild black hole, including shifts in orbit stability and frequency, providing insights into self-force effects in curved spacetime.

Contribution

It presents the first detailed computation of scalar self-force effects on various orbits around a Schwarzschild black hole, including the innermost stable circular orbit.

Findings

Self force is outward for circular orbits, decreasing angular frequency.

Self force reduces the precession rate of slightly eccentric orbits.

Self force shifts the ISCO inward by 0.122701 q^2/mu and increases its frequency by 0.0291657 q^2/mu M.

Abstract

For a particle of mass mu and scalar charge q, we compute the effects of the scalar field self-force upon circular orbits, upon slightly eccentric orbits and upon the innermost stable circular orbit of a Schwarzschild black hole of mass M. For circular orbits the self force is outward and causes the angular frequency at a given radius to decrease. For slightly eccentric orbits the self force decreases the rate of the precession of the orbit. The effect of the self force moves the radius of the innermost stable circular orbit inward by 0.122701 q^2/mu, and it increases the angular frequency of the ISCO by the fraction 0.0291657 q^2/mu M.