On Supersymmetric D-brane probes in 4d N=2 AdS₂² Attractors

We extend the $κ$-symmetry analysis of supersymmetric D-brane probes in the AdS₂ × S² attractor geometry, originally performed by Simons, Strominger, Thompson, and Yin, to also include stationary -- but non-static -- worldlines carrying angular momentum along the 2-sphere. We demonstrate that certain special trajectories, with fixed radius and orbital velocity, solve the equations of motion and moreover satisfy a supersymmetry preserving condition, thus defining new 12-BPS configurations. Furthermore, these classical paths are shown to saturate a lower bound for the Hamiltonian generating global time translations, with the corresponding minimal energy depending on a generalized angular momentum vector J. The direction of the latter, in turn, determines exactly which supercharges remain unbroken. Our results reveal a richer spectrum of (multi-particle) supersymmetric states in AdS₂ × S², which can be organized into distinct selection sectors labeled by the conserved $SU(2)$ charges. This construction has direct applications in black hole microstate counting, the analysis of probe dynamics and AdS₂/CFT₁ holography.