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

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.