Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Euler–Heisenberg electrodynamics

Abstract

We compute the quasinormal modes of massive scalar and Dirac fields within the framework of asymptotically de Sitter black holes in Euler–Heisenberg non-linear electrodynamics. We pay particular attention to the regime $$\mu M/m_{P}^2 \gg 1,$$ μ M / m P 2 ≫ 1 , where $$\mu $$ μ and M denote the masses of the field and the black hole, respectively, and $$m_{P}$$ m P represents the Planck mass, covering a range from primordial to large astrophysical black holes. Through time-domain integration, we demonstrate that, contrary to the asymptotically flat case, the quasinormal modes also dictate the asymptotic decay of fields. Employing the 6th order WKB formula, we derive a precise analytic approximation for quasinormal modes in the regime $$\mu M/m_{P}^2 \gg 1$$ μ M / m P 2 ≫ 1 without resorting to expansion in terms of the inverse multipole number. This analytic expression takes on a concise form in the limit of linear electrodynamics, represented by the Reissner–Nordström black holes. Our numerical analysis indicates the stability of the fields under consideration against linear perturbations.