Optimal escape from circular orbits around black holes

TL;DR

This paper applies the theory of optimal rocket trajectories in general relativity to determine the conditions under which a tangential acceleration is optimal for escaping stable circular orbits around black holes, revealing bounds on the acceleration.

Contribution

It extends the theory of optimal rocket trajectories to Schwarzschild spacetime, identifying when tangential maneuvers are optimal for orbit escape.

Findings

Tangential acceleration is optimal only below a certain magnitude.

The 'obvious' escape maneuver is optimal under specific conditions.

Derived bounds on acceleration magnitude for optimal escape.

Abstract

Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we show that the "obvious" manoeuvre of using a tangential instantaneous acceleration to escape a stable circular orbit in the Schwarzschild spacetime satisfies the optimality conditions if and only if the magnitude of the acceleration is smaller than a certain bound.