The quantum description of gravity demands unification of general relativity and Heisenberg uncertainty principle, which leads to the uncertainty of measurement of position itself. This means that we have to change our assumption that space-time is a smooth manifold and start to realize it as some discretized manifold, naturally described as non-commutative space. Within this description new mathematical methods are used and the notions of generalized symmetries, described with Hopf algebras are introduced. The most interesting type of non-commutative space is κ-Minkowski space, which is a Lie type deformation of usual Minkowski space. The main goal is to investigate the particle dynamics in such non-commutative space using the generalization of "Feynman approach". Since black hole physics plays an important role in investigation of quantum aspects of gravity, it is of significant interest to study its non-commutative generalizations. It was shown that non-commutative versions of different black holes (BTZ, Kerr) are completely described by κ-deformed algebras, which indicates a certain universality of κ-deformations as a candidate for describing quantum gravity effects.