Strategies of motion under the black hole horizon

Author:

Toporensky A. V.12,Zaslavskii O. B.23

Affiliation:

1. Sternberg Astronomical Institute, Faculty of Physics, Higher School of Economics, Lomonosov Moscow State University, Moscow, Russia

2. Kazan Federal University, Kremlevskaya 18, Kazan 420008, Russia

3. Department of Physics and Technology, Kharkov V.N. Karazin National University, 4 Svoboda Square, Kharkov 61022, Ukraine

Abstract

In this methodological paper, we consider two problems an astronaut faces under the black hole horizon in the Schwarzschild metric. (1) How to maximize the survival proper time. (2) How to make a visible part of the outer universe as large as possible before hitting the singularity. Our consideration essentially uses the concept of peculiar velocities based on the “river model.” Let an astronaut cross the horizon from the outside. We reproduce from the first principles the known result that point (1) requires that an astronaut turn off the engine near the horizon and follow the path with the momentum equal to zero. We also show that point (2) requires maximizing the peculiar velocity of the observer. Both goals (1) and (2) require, in general, different strategies inconsistent with each other that coincide at the horizon only. The concept of peculiar velocities introduced in a direct analogy with cosmology and its application for the problems studied in this paper can be used in advanced general relativity courses.

Publisher

World Scientific Pub Co Pte Lt

Subject

Space and Planetary Science,Astronomy and Astrophysics,Mathematical Physics

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