Classical polymerization of the Schwarzschild metric

TL;DR

This paper explores how classical polymerization modifies the Schwarzschild metric, leading to a dark energy-like energy-momentum tensor and affecting black hole thermodynamics.

Contribution

It introduces a classical polymerization approach to the Schwarzschild metric, revealing modifications that mimic dark energy and alter thermodynamical properties.

Findings

Polymer-corrected Schwarzschild metric exhibits dark energy features.

Modifications impact black hole thermodynamics.

Classical polymerization provides a new perspective on black hole geometry.

Abstract

We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a way that a transformation maps classical variables to their polymeric counterpart. We show that the usual Schwarzschild metric can be extracted from a Hamiltonian function which in turn, gets modifications due to the classical polymerization. Then, the polymer corrected Schwarzschild metric may be obtained by solving the polymer-Hamiltonian equations of motion. It is shown that while the conventional Schwarzschild space-time is a vacuum solution of the Einstein equations, its polymer-corrected version corresponds to an energy-momentum tensor that exhibits the features of dark energy. We also use the resulting metric to investigate some thermodynamical quantities associated to the Schwarzschild black hole, and in comparison with the standard Schwarzschild metric the similarities and differences are discussed.