Could the real (not virtual) static observer exist outside a Schwarzschild black hole?

TL;DR

This paper explores whether a real, static observer can exist outside a Schwarzschild black hole by analyzing a self-consistent model of observers using photon rockets to maintain fixed positions, considering back reaction effects.

Contribution

It introduces a self-consistent model of static observers outside a Schwarzschild black hole using photon rockets, accounting for back reaction and fuel consumption over infinite time.

Findings

Observers can theoretically maintain fixed positions outside the black hole.

The process of reducing mass to zero takes infinitely long.

Back reaction effects are crucial for a consistent model.

Abstract

The aim of this Letter is rather pedagogical. We considered the static spherically symmetric ensemble of observers, having finite bare mass and trying to measure geometrical and physical properties of the environmental static (Schwarzschild) space-time. It is shown that, using the photon rockets (which the mass together with the mass of their fuel is also taken into account) they can managed to keep themselves on the fixed value of radius. The process of diminishing the total bare mass up to zero lasts infinitely long time. It is important that the problem is solved self-consistently, i.e., with full account for the back reaction of both bare mass and radiation from rockets on the space-time geometry.