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.

14 pages, 6 figures, revised version

References in corpus (15)

• Loop Quantum Dynamics of the Schwarzschild Interior
• Polymer Quantum Mechanics and its Continuum Limit
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Trace Anomaly in Quantum Spacetime Manifold
• Polymer Schwarzschild black hole: An effective metric
• Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
• Black Hole Entropy, Loop Gravity, and Polymer Physics
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Graceful exit via polymerization of pre-big bang cosmology
• TeV Scale Lee-Wick Fields out of Large Extra Dimensional Gravity
• Thermostatistics of the Polymeric Ideal Gas
• Entropy in the Classical and Quantum Polymer Black Hole Models
• Polymer quantization versus the Snyder noncommutative space
• Bouncing scalar field cosmology in the polymeric minisuperspace picture

Cited by in corpus (12)

• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• (b,v)-type variables for black to white hole transitions in effective loop quantum gravity
• Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition
• Quasinormal modes of a holonomy corrected Schwarzschild black hole
• Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model
• Gravitational lens effect of a holonomy corrected Schwarzschild black hole
• Effective Quantum Dust Collapse via Surface Matching
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Quantum Corrected Polymer Black Hole Thermodynamics: Mass Relations and Logarithmic Entropy Correction
• Gravitational lensing in holonomy corrected spherically symmetric black holes with phantom global monopoles
• Generic features of a polymer quantum black hole
• Affine quantization of the dynamical Reissner--Nordström region