Dirac QNM spectrum from twisted semiclassical gauge theory of gravity

Twisted Abelian gauge theory coupled to a noncommutative (NC) Dirac field is studied in order to infer the quasinormal mode (QNM) spectrum of the fermion matter perturbations in the vicinity of the Reissner-Nordstr\"om (RN) black hole. The action functional of the theory is invariant under the truncated NC local $U(1)_{\star}$ gauge transformations that keep the gravitational background intact. The latter, being a classical gravitational background unaffected by the NC local gauge transformations, makes the theory semiclassical. The most prominent feature of the QNM spectrum is the splitting in the total angular momentum projection due to the noncommutativity induced $SO(3) \rightarrow U(1)$ symmetry breaking pattern.