How to Delay Death and Look Further Into the Future if You Fall Into a Black Hole

In this note, we present a pedagogical illustration of peculiar properties of motion in the vicinity of and inside black holes. We discuss how a momentary impulse can modify the life-time 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 the personal lifetime of a falling observer) till the contact with the singularity, as well as the time interval in the Lemaître 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 an engine with a finite power. This example is suitable for university seminars for undergraduate students specializing in general relativity and related astrophysical subjects.