Probing quantum spacetime with Dirac quasinormal modes

Abstract Noncommutative (NC) geometry may open an alternative route to quantum gravity. We study the signatures that quantum structure of spacetime may leave on Dirac quasinormal mode spectrum in the setting defined by a common astrophysical background. For that purpose we examine the influence of spacetime noncommutativity on the Dirac quasinormal modes in modified Reissner–Nordström black hole spacetime. The framework for the latter study is provided by the effective model of NC gravity coupled to fermions introduced in Dimitrijević Ćirić et al. (Eur Phys J C 83:387, 2023). This model describes a classical Dirac field coupled to a modified Reissner–Nordström geometry where the corresponding metric acquires an additional nonvanishing $$r-\varphi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> <mml:mi>φ</mml:mi> </mml:mrow> </mml:math> component. As the earlier study shows, this model appears to be equivalent to a model of semiclassical NC gauge theory in which a NC gauge field is coupled to a NC fermion field on the one side and the classical Reissner–Nordström background on the other. We compute the resulting Dirac quasinormal modes and compare them with those of the undeformed Reissner–Nordström spacetime. The results show that spacetime noncommutativity modifies both the oscillation frequencies and damping rates, and induces features in the effective potential and quasinormal mode spectrum reminiscent of a Zeeman-like splitting. Since such geometric modifications are expected to become relevant only near the Planck scale, these effects are more naturally associated with microscopic rather than astrophysical black holes.