The twin paradox in the vicinity of rotating black holes

Abstract

The twin paradox is a foundational thought experiment in the special theory of relativity where a returning twin ages less than the one who remains stationary. However, the intricacies of the twin paradox remain relatively underexplored in the curved spacetimes of general relativity. Here we explore the twin paradox in the vicinity of a rotating black hole, where the existence of multiple paths between two events creates significant complexity. We develop a numerical framework based on residual maps and optimisation to identify possible trajectories. We find a strong negative correlation between a traveller's experienced proper time and both the azimuthal distance travelled and the magnitude of acceleration. We apply numerical Jacobi field analysis to examine conjugate points along geodesics within the Kerr geometry, finding that only the geodesic with the minimal azimuthal distance contains no conjugate points. This provides beginner students of general relativity with a visual tool to understand general relativistic concepts, helping to correct flat-spacetime intuitions.