Kerr-referenced analytical parametrization of rotating black holes in dynamical Chern-Simons gravity

Abstract

Rotating black holes in dynamical Chern-Simons gravity are known nonperturbatively mainly through numerical solutions, which limits their direct use in strong-field applications. We construct a Kerr-referenced analytical parametrization of the near-general-relativistic numerical branch using a compact radial coordinate, low-order angular multipoles, and continued fractions. The resulting two-parameter family accurately reproduces the numerical metric throughout the validated weak-coupling and moderate-spin domain. Independent off-grid solutions confirm that the parametrization retains its accuracy away from the calibration set. We further assess the model through equatorial light rings, critical impact parameters, and full two-dimensional null-geodesic ray tracing without assuming separability. The resulting shadow observables closely match those obtained from the numerical geometries. This parametrization therefore provides a practical analytical metric for geodesic and strong-field calculations without relying on a slow-rotation expansion.