Quantum probing of singularities at event horizons of black holes

TL;DR

This paper demonstrates that changing coordinates in the Schwarzschild metric does not remove the quantum 'fall' mode at a black hole's event horizon, challenging assumptions about stationary quantum states near black holes.

Contribution

It shows that coordinate transformations cannot eliminate the quantum fall mode at the event horizon, highlighting a fundamental issue in black hole quantum mechanics.

Findings

Coordinate transformations do not remove the fall mode.

The fall mode is incompatible with stationary quantum states.

Implications for quantum theory near black hole horizons.

Abstract

It is proved that coordinate transformations of the Schwarzschild metric to new static and stationary metrics do not eliminate the mode of a particle ''fall'' to the event horizon of a black hole. This mode is unacceptable for the quantum mechanics of stationary states.