Probing the regular spacetime with an asymptotically Minkowski core by precessing motion

Abstract

Following the works of Rahaman et al. (2018) and Chen et al. (2024) in which the dyon black holes and covariant loop quantum black holes were respectively taken as effective descriptions of the exterior field of the Sun and tested by the motion of planets of the Solar System, we hypothesize that the exterior solution of a regular black hole with an asymptotically Minkowski core might be adopted to describe the external field of a spherical celestial body featuring a suppression parameter $\ell$ and constrain such a parameter. We calculate the first-order post-Newtonian relativistic periastron advance of a timelike particle in this spacetime. We then test this model in the five binary pulsars and Solar System, determining its upper limits as $\ell \sim 10^{-2}m$. Compared with the result of $\ell \sim 10^{8}m$ obtained from the shadow of Sgr A*, our result is improved by 10 orders of magnitude.