Horizon Quantum Mechanics for spheroidal sources

TL;DR

This paper extends Horizon Quantum Mechanics to spheroidal sources, analyzing trapping surfaces and proposing a method to determine deformation parameters in the quantum framework.

Contribution

It introduces an extension of Horizon Quantum Mechanics to spheroidal geometries and offers a way to quantify deformation parameters quantum mechanically.

Findings

Misner-Sharp mass accurately locates horizons in spheroidal deformations

Deformation parameter can be determined within the quantum theory framework

Trapping surfaces are characterized in axial deformed space-times

Abstract

We start investigating the extension of the Horizon Quantum Mechanics to the case of spheroidal sources. We first study the location of trapping surfaces in space-times resulting from an axial deformation of static isotropic systems, and show that the Misner-Sharp mass evaluated on the corresponding undeformed spherically symmetric space provides the correct gravitational radius to locate the horizon. We finally propose a way to determine the deformation parameter in the quantum theory.