Black Holes in Proca-Gauss-Bonnet Gravity with Primary Hair: Particle Motion, Shadows, and Grey-Body Factors

TL;DR

This paper explores black holes in Proca-Gauss-Bonnet gravity, analyzing their properties, particle dynamics, shadows, and grey-body factors, revealing significant deviations from Schwarzschild black holes with strong coupling parameters.

Contribution

It introduces new asymptotically flat black hole solutions with primary hair in Proca-Gauss-Bonnet gravity and studies their observable signatures and perturbation characteristics.

Findings

QNM-based grey-body factors are accurate for high multipole numbers.

Deviations from Schwarzschild become significant with larger Proca hair and couplings.

Characteristic observables like shadow radius and ISCO are computed for these black holes.

Abstract

We investigate classical and semiclassical signatures of black holes in a recently proposed Proca-Gauss-Bonnet gravity model that admits asymptotically flat solutions with primary hair. Two distinct classes of spherically symmetric metrics arise from different relations between the coupling constants of scalar-tensor and vector-tensor Gauss-Bonnet interactions. For each geometry, we examine the range of parameters permitting horizon formation and analyze the motion of test particles and light rays. We compute characteristic observables including the shadow radius, Lyapunov exponent, innermost stable circular orbit (ISCO) frequency, and binding energy. Additionally, we study scalar and Dirac field perturbations, derive the corresponding effective potentials, and calculate the grey-body factors (GBFs) using both the sixth-order Wentzel-Kramers-Brillouin (WKB) method and their correspondence with quasinormal modes (QNMs). Our results show that the QNM-based approximation of GBFs is accurate for sufficiently large multipole numbers and that deviations from Schwarzschild geometry become pronounced for large values of the Proca hair and Gauss-Bonnet couplings.