Using the first law of thermodynamics, we propose a relation between the system entropy ( S) and its IR ( L) and UV ([equation]) cutoffs. In addition, applying this relation to the apparent horizon...

Over the last few years, Planck-scale modifications to the dispersion relation of particles have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications [F. Girelli, S. Liberati, and L. Sindoni, Phys. Rev. D 75, 064015 (2007)] that Finsler geometry can provide some generalization of Riemannian geometry which may allow us to account for the nontrivial (Planckian) structure of the relativistic particles’ configuration space. We investigate the possibility to formalize Planck-scale deformations to relativistic models in curved spacetime, within the framework of Finsler geometry. We take into account the general strategy of analysis of dispersion relations modifications in curved spacetimes proposed in [G. Rosati, G. Amelino-Camelia, A. Marciano, and M. Matassa, Phys. Rev. D 92, 124042 (2015)], generalizing to the de Sitter case the results obtained in [G. Amelino-Camelia, L. Barcaroli, G. Gubitosi, S. Liberati, and N. Loret, Phys. Rev. D 90, 125030 (2014)] for deformed relativistic particle kinematics in flat spacetime using Finsler formalism.

The spacetime solution for a black hole, surrounded by an exotic matter field, in Rastall gravity, is calculated in an arbitrary d-dimensional spacetime. After this, we calculate the scalar quasinorma

Planck scale modified dispersion relations are one way to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer’s or particle’s proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $\kappa$-Poincaré dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the $\kappa$-Poincaré dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon’s lifetime.