DSR-GUP, maximally localized state, and black hole thermodynamics

Abstract

We consider a new type of doubly special relativity transformation which gives a new types of generalized uncertainty principle. This model is known to have invariant Planck energy (or Planck momentum) and minimal length. For this model we discuss the generalized uncertainty relation and compute the minimal length and momentum upper bound. We also compute the corresponding maximally localized state explicitly. Finally, we use the generalized uncertainty relation compatible with doubly special relativity to discuss black hole thermodynamics.