Lifshitz scalar, brick wall method, and GUP in Hořava-Lifshitz Gravity

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

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 un…