The infalling photon, the infalling particle, and the observer at rest near the horizon of a black hole

TL;DR

This paper examines the divergent energy measurements of infalling particles and photons near a black hole horizon, clarifying the physical significance of these divergences and their impact on black hole geometry.

Contribution

It demonstrates that the observer at rest near the horizon can induce metric corrections unless their mass is negligible, addressing misconceptions about energy divergence.

Findings

Energy diverges for infalling particles near the horizon

Observer's mass influences metric corrections

Divergences do not necessarily alter black hole geometry

Abstract

When a massive test particle or a photon fall radially into a black hole, their energy, as measured by a static observer located very close to the horizon, diverges. In introductory courses on General Relativity, this fact gives rise to questions about the reality of this divergence, and its eventual effect on the geometry of the black hole. We address these concerns and show that, eventually, it is the observer at rest who may induce corrections to the metric, unless its mass is crucially small when located near the horizon.