Classical polymerization of the Schwarzschild metric

Understand

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.