Higher Dimensional Loop Quantum Black hole in de Sitter Spacetime: Quasinormal Modes and Shadow Signatures

Abstract

We investigate the dynamical and optical properties of a higher-dimensional loop-quantum-corrected black hole in a de Sitter background. We first analyze the horizon structure and identify the admissible nonextremal black-hole domain bounded by the extremal and Nariai configurations, ensuring the existence of distinct inner, event, and cosmological horizons for the parameter sets considered. We then examine the scalar effective potential and show that the loop-quantum correction deforms the classical scattering barrier primarily in the strong-field region while preserving its characteristic single-barrier structure. The quasinormal modes of massless scalar perturbations are computed using time-domain evolution with Prony extraction, the matrix method, and the WKB approximation, showing good agreement among the three approaches. The time-domain waveform and its Prony and matrix-frequency reconstructions provide an additional direct consistency check of the extracted ringdown spectrum. We find that loop quantum corrections induce moderate shifts in the quasinormal spectrum, whereas the spacetime dimensionality has a much stronger impact, leading to higher oscillation frequencies and damping rates. The negative imaginary parts of all modes indicate dynamical stability against massless scalar perturbations within the explored parameter range. Comparison with the corresponding classical black-hole backgrounds shows that the quantum-corrected quasinormal spectrum remains continuously connected to the classical photon-sphere branch, with the loop correction producing quantitative rather than qualitative changes.

Comments: 31 pages, 12 figures and 5 tables