Prolonging The Inevitable: Maximising survival time of an engine-equipped spacecraft between spatial hypersurfaces, as applied to the Schwarzschild spacetime

TL;DR

This paper investigates how long a spacecraft with propulsion can survive inside a Schwarzschild black hole's event horizon, providing analytical formulas, optimal strategies, and generalizations to other spacetimes.

Contribution

It introduces a method to calculate maximum survival time with propulsion in Schwarzschild spacetime and proposes an optimal control strategy to extend life.

Findings

Derived analytical expressions for survival time as elliptic integrals.

Proved a principle for optimal propulsion strategy to maximize survival.

Quantified survival time gains under realistic conditions.

Abstract

The fate of an astronaut unfortunate -- or foolish -- enough to find themselves hurtling towards spaghettification after passing the event horizon of a black hole is a common anecdote told by scientists to the regular population. However, despite the fact the Schwarzschild spacetime has been discovered over a century ago, the simple question of how long can such a space traveller live has not been fully elaborated on since. In fact, a few textbooks even give a mistaken or easily misread description of what happens. We address those inconsistencies. We calculate the proper time a space traveller equipped with means of propulsion can expect to live in these circumstances, giving analytical expressions (as elliptic integrals) wherever possible. We prove a principle that explains the best strategy to extend their life, and show its' generalisation for other spacetimes. Finally, we give quantitative answers to what gains due to optimal control can be expected in typical and somewhat `realistic' circumstances.