# On strategies of motion under the black hole horizon

## TL;DR

This paper explores optimal strategies for an astronaut inside a black hole horizon to maximize survival time and visibility of the outside universe, using the river model and peculiar velocities, revealing conflicting approaches for each goal.

## Contribution

It introduces a novel application of peculiar velocities within the river model to analyze motion strategies under the black hole horizon, providing new insights into survival and observational optimization.

## Key findings

- Turning off the engine near the horizon maximizes survival time.
- Maximizing peculiar velocity enlarges visible universe before singularity.
- Strategies for survival and visibility are fundamentally incompatible.

## Abstract

In this methodological paper we consider two problems an astronaut faces with 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 the present paper can be used in advanced general relativity courses.