The quantum black hole as a theoretical lab, a pedagogical treatment of a new approach

TL;DR

This paper presents a pedagogical approach to quantised black holes, emphasizing the importance of strict logical rules and one-to-one state mappings, offering new insights into space-time topology without relying on string theory or AdS/CFT.

Contribution

It introduces a novel method for quantising black holes based on strict logical consistency and state mapping, avoiding assumptions like string theory.

Findings

Highlights the non-triviality of space-time topology near black holes

Proposes a consistent quantum state mapping between observers

Provides a framework independent of string theory or AdS/CFT

Abstract

Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects particles outside the hole) with the observations of a local observer (who falls into a black hole) must map the quantum states in a one-to-one way. This does not come out right if one follows text book rules. Here it is advocated that demanding very strict logic leads to new insights, such as the non-triviality of space-time topology near a black hole. This way one may attempt to make up for the lack of direct experimental evidence concerning gravitation at the Planck scale. It is noted that this approach does not require assumptions such as string theories or AdS/CFT conjectures. All we need to assume is the validity of quantum field theory wherever the Schwarzschild metric is regular, combined with the requirement that only those general coordinate transformations apply that map pure quantum states one-to-one onto pure quantum states.