Eikonal Ringing, Shadows, Lensing, Grey-Body Factors, and Binding Energy of Asymptotically Flat Regular Black Holes in Phantom Dirac-Born-Infeld Gravity

Abstract

We develop a geodesic-optics description of eikonal quasinormal ringing, blackhole shadows, strong lensing, grey-body factors (GBFs), and the binding energy of massive particles for the asymptotically flat regular black-hole geometry obtained in phantom Dirac-Born-Infeld (DBI) gravity. The null-orbit structure admits an especially compact analytic treatment. The unstable photon orbit remains at the Schwarzschild-like coordinate radius throughout the black-hole branch, while the orbital frequency and Lyapunov exponent coincide exactly. Consequently, eikonal quasinormal modes (QNMs), shadow radius, GBFs, and strong-deflection observables are all governed by a single dimensionless function of the core-size parameter. For timelike circular motion, we derive exact expressions for the specific energy and angular momentum, obtain the innermost stable circular orbit (ISCO) condition in closed implicit form, and show that the ISCO binding efficiency decreases as the regular core grows. We present illustrative plots for the exact geodesic invariants, the corresponding grey-body profiles, and the timelike binding-energy curves. The resulting construction provides an exact one-parameter bridge between the regular black-hole metric and its leading geodesic observables.