Event Detection and Finite-Grid Effects at an Imposed Absorbing Boundary in Newtonian Black Hole Orbit Integrations

Numerical classification of black-hole orbits can depend on how prescribed inner capture or absorbing boundaries are implemented. This study investigated how discrete evaluation of such a boundary affects orbit classification. Massless particles were integrated about an isolated Newtonian point mass and initialized at periapsis with an absorbing boundary at rsink = 104RS. Because the Keplerian periapsis q is constant, the expected classification can be analytically determined. A classifier omitting evaluation at initialization can miss particles that already satisfy the removal criterion, but evaluation at t = 0 reproduced the analytic classification on every sampled grid. As the grid resolution increased, the inferred critical periapsis approached the imposed sink radius. These results demonstrate that an apparent critical periapsis can depend on both the imposed boundary and its numerical evaluation, emphasizing the need to distinguish numerical effects from genuine dynamical thresholds.