Orbital, Shadow, and Thin-Disk Signatures of a Regular Black Hole with Gravitational Self-Energy

Abstract

We investigate geodesic motion, shadow observables and thin-disk accretion for the regular black hole generated by a non-local gravitational self-energy contribution. The geometry is controlled by a zero-point length and can be followed smoothly from the Schwarzschild limit to a cold extremal remnant. We compute the photon ring, critical impact parameter, apparent shadow radius, null Lyapunov exponent, innermost stable circular orbit, orbital frequencies and Novikov-Thorne flux profile. As the self-energy scale grows, both the photon ring and the ISCO move outward, while the photon-ring frequency and instability exponent decrease. The horizon-normalized shadow area increases by about a factor of 2.7 for the near-extremal benchmark, although the same shadow radius decreases when normalized by the ADM mass. The ISCO binding efficiency grows modestly, whereas the zero-torque thin-disk flux peak moves outward and falls to about 61% of the Schwarzschild peak as the solution approaches the remnant regime. These trends identify a coherent set of optical, orbital and accretion signatures of the gravitational-self-energy regularization.