Probing the regular black hole with an asymptotically Minkowski core by precessing motion of S2 star and OJ 287

Abstract We investigate the precessing motion around the the regular black hole with an asymptotically Minkowski core which has a suppression parameter $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> . We obtain the third-order post-Newtonian quasi-Keplerian motion of a test particle in this spacetime and find its relativistic periastron advance. Then, we test this model with the precessing motion of the star S2 and of OJ 287 and determine the upper limits of the dimensionless suppression parameter as $$\ell /m \sim 10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , where m is the mass of the black hole. Compared with the bound given by the shadow of Sgr A*, our bound on $$\ell /m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> is reduced by 2 orders of magnitude, although our upper limit of $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> still needs further improvement.