Towards gravitational QNM spectrum from quantum spacetime

Abstract

The effective potential for the axial mode of gravitational wave on noncommutative Schwarzschild background is presented. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a semi-Killing Drinfeld twist. The analysis is performed up to the first order in perturbation of the metric and noncommutativity parameter. This results in a modified Regge-Wheeler potential with the strongest differences in comparison to the classical Regge-Wheeler potential being near the horizon.

9 pages, 1 figure; presented and prepared for "the XII. International Symposium on Quantum Theory and Symmetries" (QTS12) and "XXVII. International Conference on Integrable Systems and Quantum Symmetries" (ISQS27),July 24-28 2023., Prague