How to delay death and look further into the future if you fall into a black hole

TL;DR

This paper explores how impulses can extend the perceived lifetime of objects falling into black holes and how to maximize the observable future from within, using pedagogical examples in general relativity.

Contribution

It provides a detailed analysis of how finite impulses can alter the proper and external time intervals for objects falling into Schwarzschild black holes, highlighting strategies to delay death.

Findings

A finite impulse can significantly increase the proper lifetime before reaching the singularity.

The maximum external future a falling observer can perceive depends on the impulse received.

Strategies to optimize the timing intervals involve finite-power engines.

Abstract

In this note, we present a pedagogical illustration of peculiar properties of motion in the vicinity and inside black holes. We discuss how a momentary impulse can modify the lifetime of an object radially falling into a Schwarzschild black hole down to singularity. The well known upper limit for a proper time spent within a horizon, in fact, requires an infinitely powerful kick. We calculate the proper time interval (perceived as personal lifetime of a falling observer) till the contact with the singularity, as well as the time interval in the Lema\^itre frame (which reflects how far into the future of the outer world a falling observer can look), for different values of the kick received by the falling body. We discuss the ideal strategy to increase both time intervals by the engine with a finite power. This example is suitable for university seminars for undergraduate students specializing in General Relativity and related astrophysical subjects.