We study the dynamical and scattering properties for the Euler-Heisenberg black holes surrounded by perfect fluid dark matter. The geometry contains a compact nonlinear electrodynamic correction governed by the Euler-Heisenberg coupling and a logarithmic dark-matter contribution governed by the surrounding perfect fluid dark matter (PFDM) halo. We study the scalar, electromagnetic, and a particular effective axial spin-2 channel constructed on the fixed Euler-Heisenberg plus PFDM background, acting as a proxy for the gravitational-like perturbation problem and not for the fully coupled gravitational perturbation problem. We compute the quasinormal-mode spectrum employing a 13th-order Wentzel-Kramers-Brillouin method supplemented with Padé resummation and compare it with the eikonal prediction calculated in terms of the angular frequency of the photon sphere and the Lyapunov exponent. Moreover, we study the near-extremal configurations and derive a purely imaginary branch of quasinormal frequencies in the near-horizon region, whose damping rate increases with the PFDM parameter and is nearly spin independent. We then compute exact graybody factors by direct numerical integration of the radial wave equation and compare them to analytical lower bounds. We also analyze the absorption cross sections and the Hawking emission spectra. We also calculate the relativistic enhancement of the neutrino-antineutrino annihilation channel $\nu \overline{\nu }\to e^{-}{e}^{+}$ outside the Euler-Heisenberg-PFDM black hole. We find that the PFDM parameter contracts the optical structure, increases the oscillation frequency, enhances the damping rate, and suppresses transmission. On the other hand, the Euler-Heisenberg correction leads to a weaker near-horizon deformation whose effect becomes relevant for sufficiently large charge. These results provide a common scattering framework for comparing the impact of dark-matter environments and nonlinear electrodynamics on black-hole spectroscopic and radiative observables.

Close

PrevNext

View figure in article

• General relativity