Linear and Quadratic GUP, Liouville Theorem, Cosmological Constant, and Brick Wall Entropy

Abstract

Motivated by the works on Equivalence Principle in the context of linear Generalized Uncertainty Principle and, independently, in the context of quadratic Generalized Uncertainty Principle, we expand these endeavors in the context of Generalized Uncertainty Principle when both linear and quadratic terms in momentum are include. We demonstrate how the definitions of equations of motion change upon that expansion. We also show how to obtain an analogue of Liouville theorem in the presence of linear and quadratic Generalized Uncertainty Principle. We employ the corresponding modified invariant unit volume of phase space to discuss the resulting density of states, the problem of cosmological constant, the black body radiation in curved spacetime, the concurrent energy and consequent no Brick Wall entropy.

v1: 10 pages, RevTex, 7 figures; v2: references updated, one footnote added; v3: two footnotes and references added, no change in physics, to appear in EPJC

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• Modified Brans-Dicke cosmology with Minimum Length Uncertainty
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• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Szekeres Universes with GUP corrections
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• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
• Quantum Gravity Corrections to the Mean Field Theory of Nucleons
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• Proton Decay and the Quantum Structure of Spacetime