Quasinormal modes and Hawking radiation of black holes with primary scalar hair
Phys. Rev. D 114, 084048 – Published 19 October, 2026
DOI: https://doi.org/10.1103/qpj1-rw5b
Abstract
Recently, a new family of asymptotically flat black-hole solutions endowed with primary scalar hair has been discovered in beyond-Horndeski gravity. We study in detail the quasinormal modes spectra, graybody factors, and Hawking radiation of this class of black holes. We demonstrate that the presence of primary scalar hair leaves characteristic imprints on the ringdown properties and shifts the quasinormal frequencies, inducing overtone rearrangements and the rise of echoes. While the fundamental modes associated with the light ring are affected moderately, higher overtones are highly sensitive to the small near-horizon deformation produced by the scalar field. In certain parameter regimes, the graybody factors exhibit resonant-tunneling behavior, which leads to an oscillatory frequency dependence of the Hawking emission rate. Thus, both black-hole spectroscopy and Hawking radiation may provide complementary and distinctive probes of the beyond-Horndeski gravity. Additionally, we demonstrate that the corresponding naked singularities are quantum mechanically singular, and wave dynamics is ill posed.
