Classical polymerization of the Schwarzschild metric

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.