Polymer Geodesic Motion in Schwarzschild Spacetime

TL;DR

This paper explores how polymer quantum mechanics modifies geodesic motion around Schwarzschild black holes, revealing forbidden regions near the horizon and stable orbits inside the classical ISCO, with implications for black hole phenomenology.

Contribution

It introduces a semi-classical polymer quantum framework to analyze black hole geodesics, uncovering novel stable orbits and forbidden regions near the horizon.

Findings

Existence of a classically forbidden region near the horizon.

Presence of stable circular orbits below the classical ISCO.

Altered equations of motion due to Planckian scale corrections.

Abstract

In this paper we will study the geodesic motion of massive particles, in a Schwarzschild background, with a semi-classical quantum framework called "Polymer Quantum Mechanics" (PQM) in order to investigate the black hole phenomenology resulting from this formulation, which accounts for Planckian scale physics. In particular we studied two main scenarios, being the radial in-fall and circular orbits and their stability. In this framework, we built an effective Hamiltonian taking into account the polymer quantum effects, altering the classical equations of motion with Planckian scale corrections. As a main result, we obtained the existence of a classically forbidden region surrounding the event horizon, preventing particles from crossing it. Additionally, we discovered the presence of stable circular orbits below both the classical Innermost Stable Circular Orbit (ISCO) and the horizon (corresponding to closed time-like geodesics).