Orbital motion of primordial black holes crossing Sun-like stars

Primordial black holes (PBHs) are hypothetical objects that could have originated from density fluctuations in a very early phase of our Universe. Recent observations restrict the masses mpbh that such PBHs could have, if they are to constitute all of dark matter today: 1017 g≤ mpbh≤1023 g. With such low masses, general relativity predicts that the corresponding Schwarzschild radii rpbh=2Gmpbh/c2 for the PBHs would range from subatomic to molecular sizes, namely 10−11 cm≤rpbh≤10−5 cm. When captured by a star, such a tiny PBH could exhibit an orbit completely or partially inside the body of the star, without significantly changing its mass for quite a long time. Here, we examine the possible trajectories of a PBH that is captured by a Sun-like star. When in motion in the interior of the star, the amount of stellar mass that effectively interacts gravitationally with the PBH will be a function of its distance to the center of the star. As a consequence, a strong effect on the shape of the orbits emerges, leading to PBH trajectories that could be open or closed, and exhibiting a rich variety of patterns. In particular, orbits that traverse the interior of the host star will undergo precession, due strictly to Newtonian dynamics.