The rocket problem in general relativity

TL;DR

This paper develops covariant optimality conditions for rocket trajectories in general relativity and applies them to minimize fuel consumption in galaxy transfers and orbit changes.

Contribution

It introduces a covariant framework for optimal rocket trajectories in general relativity and solves specific transfer problems in cosmological and black hole spacetimes.

Findings

Derived covariant optimality conditions for rocket trajectories.

Solved minimum fuel transfer problems in FLRW and Schwarzschild spacetimes.

Abstract

We derive the covariant optimality conditions for rocket trajectories in general relativity, with and without a bound on the magnitude of the proper acceleration. The resulting theory is then applied to solve two specific problems: the minimum fuel consumption transfer between two galaxies in a FLRW model, and between two stable circular orbits in the Schwarzschild spacetime.