Polymeric Quantization and Black Hole Thermodynamics

Abstract

Polymer quantization is a non-standard representation of the quantum mechanics that inspired by loop quantum gravity. To study the associated statistical mechanics, one needs to find microstates' energies which are eigenvalues of the Hamiltonian operator in the polymer framework. But, this is not an easy task at all since the Hamiltonian takes a nonlinear form in polymer picture. In this paper, we introduce a semiclassical method in which it is not necessary to solve the eigenvalue problem. Instead, we work with the classical Hamiltonian function and the deformed density of states in the polymeric phase space. Implementing this method, we obtain the canonical partition function for the polymerized systems and we show that our results are in good agreement with those arising from full quantum considerations. Using the partition function, we study the thermodynamics of quantum Schwarzschild black hole and we obtain corrections to the Bekenstein-Hawking entropy due to loop quantum gravity effects.

13 pages, no figures, revised for PLB, title changed

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Cited by in corpus (17)

• Semiclassical corrections to black hole entropy and the generalized uncertainty principle
• A new bound on polymer quantization via an opto-mechanical setup
• High temperature dimensional reduction in Snyder space
• Quantum Mechanical Corrections to the Schwarzschild Black Hole Metric
• Some Astrophysical Aspects of a Schwarzschild Geometry Equipped with a Minimal Measurable Length
• Thermostatistics of the Polymeric Ideal Gas
• Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD
• The Quantum Field Theory Boundaries Applicability and Black Holes Thermodynamics
• Classical polymerization of the Schwarzschild metric
• Polymer quantization versus the Snyder noncommutative space
• Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
• Discrete spectrum of the quantum Reissner - Nordström geometry
• Polymer quantum effects on compact stars models
• Noncommutative spaces and covariant formulation of statistical mechanics
• Photon gas thermodynamics in dS and AdS momentum spaces
• Ideal Quantum Gases with Planck Scale Limitations
• Superfluids in Polymer Quantum Mechanics