Perturbations and greybody bounds of Euler-Heisenberg black holes surrounded by perfect fluid dark matter

TL;DR

This paper studies how massless fields behave around Euler-Heisenberg black holes with surrounding dark matter, analyzing potential barriers, greybody factors, and emission rates to identify effects of nonlinear electrodynamics and dark matter.

Contribution

It derives effective potentials and greybody bounds for various fields in an EH black hole with dark matter, revealing how these parameters influence black hole scattering and emission spectra.

Findings

Greybody bounds increase with frequency and approach high-frequency limits.

Dark matter and nonlinear electrodynamics significantly alter potential barriers.

The model's results differ from Schwarzschild, Reissner-Nordström, and pure EH black holes.

Abstract

We investigate the propagation of massless fields with spins $s=0$, $s=1$, and $s=1/2$ in the spacetime of an Euler-Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). This background incorporates both the nonlinear electrodynamic correction associated with the EH effective theory and the logarithmic contribution induced by the surrounding dark matter distribution. After deriving the corresponding Schr\"odinger-like radial equations, we construct the effective potentials for scalar, electromagnetic, and Dirac perturbations and analyze how they are modified by the black hole charge, the EH parameter, and the PFDM parameter. The greybody factors are estimated through the rigorous Boonserm-Visser lower-bound method, and the associated partial absorption cross sections are obtained for different spin sectors using these bounds. Our results show that the nonlinear electrodynamic and dark matter parameters significantly deform the effective potential barrier, leading to potentially distinguishable changes in the transmission probabilities and absorption spectra within the model. In particular, the greybody lower bounds increase monotonically with the frequency and approach the high-frequency limit, while their low-frequency behavior is strongly affected by the geometry and by the spin of the perturbing field. Moreover, we utilize the greybody lower bound to calculate the energy emission rate. Finally, we make comparisons with the Schwarzschild, Reissner-Nordstr\"om, and pure EH limits, showing that the combined EH+PFDM background produces distinguishable corrections to black-hole scattering within the model. These results highlight greybody bounds as sensitive diagnostic probes of nonlinear electrodynamic effects and dark matter halos around compact objects.