Scattering angle in a topological star spacetime: A self-force approach

We compute the scattering angle for a scalar neutral probe undergoing unbound motion around a topological star, including self-force effects. Moreover, we identify the ``electromagnetic'' source of the background as a Papapetrou field compatible with the isometries and characterize topological stars by studying their sectional curvature, geometric transport along special curves, and gravitational energy content in terms of the superenergy tensors.