Astrophysical observables for regular black holes with sub-Planckian curvature* *Supported in part by the Natural Science Foundation of China (11875053, 12035016). It is also supported by the Beijing Natural Science Foundation (1222031), and the Sichuan Youth Science and Technology Innovation Research Team with (21CXTD0038), Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province with (2021ZYD0032)

Abstract

We investigate the photon sphere and marginally stable circular orbit of massive particles over the recently proposed regular black holes with sub-Planckian curvature and a Minkowskian core. We derive the effective potential for geodesic orbits and determine the radius of circular photon orbits, with an analysis of the stability of these orbits. We extend our analysis to the background of a compact massive object (CMO) without a horizon, whose mass is below the lowest bound for the formation of a black hole. For massive particles, marginally stable circular orbits become double-valued in the CMO phase. Through a comparison with Bardeen and Hayward black holes, we also find that the locations of the photon sphere and marginally stable circular orbit in the CMO phase with a Minkowskian core are evidently different from those in the CMO phase with a dS core, which potentially provides a way to distinguish between these two types of black holes by astronomical observation. Finally, we present the observational constraint on the deviation parameter for such regular black holes using observed data from the black hole M87*.