q-Plane Wave Solutions of q-Weyl gravity
V. K. Dobrev, S. G. Mihov
TL;DR
The paper develops a quantum-group–symmetric, $q$-deformed formulation of linear conformal Weyl gravity by employing a noncommutative $q$-Minkowski space and the quantum conformal algebra $U_q(sl(4))$. It derives $q$-deformed d'Alembert and Weyl equations and constructs explicit $q$-plane-wave solutions that express Weyl-tensor components in vacuum, using a two-basis plane-wave formalism. The main contribution is the explicit realization of $q$-plane-wave solutions for the $q$-Weyl gravity equations and the demonstration that these solutions can be organized as deformed plane waves multiplied by momentum polynomials, while preserving the underlying quantum conformal symmetry. The work lays groundwork for extending to nonzero energy-momentum and for cross-checks with the full $q$-Weyl system, offering a potential regularization mechanism and new insights into quantum-deformed gravity.
Abstract
We give solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves.