Towards relativistic quantum geometry

TL;DR

This paper develops a gauge-invariant relativistic quantum geometry framework using Weylian-like manifolds and applies it to analyze a Reissner-Nordström black hole, highlighting observer-dependent algebra of the geometric field.

Contribution

It introduces a novel gauge-invariant relativistic quantum geometry model based on Weylian-like manifolds with a scalar field, applicable to black hole spacetimes.

Findings

Gauge-invariant quantum geometry constructed with Weylian-like manifolds

Observer-dependent algebra of the geometric scalar field

Application to Reissner-Nordström black hole geometry

Abstract

We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner-Nordstr\"om black-hole is studied.