Shadow, Quasinormal Modes, Sparsity, and Energy Emission Rate of Euler-Heisenberg Black Hole Surrounded by Perfect Fluid Dark Matter

TL;DR

This paper studies how perfect fluid dark matter influences the optical, dynamical, and radiative properties of Euler-Heisenberg black holes, highlighting dark matter's dominant role over quantum corrections in observable phenomena.

Contribution

It provides a comprehensive analysis of the effects of dark matter and black hole charge on shadow, quasinormal modes, and Hawking radiation, emphasizing dark matter's significant impact.

Findings

Dark matter significantly alters photon sphere and shadow size.

Black-hole charge affects quasinormal frequencies and emission profiles.

Euler-Heisenberg corrections are subleading but notable in strong-charge regimes.

Abstract

In this work, we investigate the optical, dynamical, and radiative properties of an Euler--Heisenberg black hole immersed in a perfect fluid dark matter (PFDM) background. We analyze the photon sphere and shadow, the scalar quasinormal-mode spectrum in the eikonal regime, the grey-body factor through the eikonal QNM correspondence, the sparsity of Hawking radiation, and the corresponding energy emission rate. Our results show that both the black-hole charge and the PFDM parameter significantly affect the photon sphere, shadow size, quasinormal frequencies, Hawking temperature, and emission profile, whereas the Euler--Heisenberg correction is typically subleading in the parameter range explored, although it may become more visible in strong-charge regimes for selected observables. Overall, the dark-matter environment provides the dominant imprint on the phenomenology of the system, indicating that shadow and ringdown-related quantities may serve as useful probes of PFDM effects within the approximations considered.