Kerr--Schild--AdS geometries in quadratic f(R) gravity: A no-go theorem

We investigate Kerr-Schild-AdS geometries in quadratic f® gravity without imposing the constant-curvature condition R=R_0 a priori. We show that the field equations dynamically enforce constant scalar curvature and uniquely select the Kerr–AdS family of solutions. Thus, quadratic f® gravity admits no Kerr–AdS solutions beyond the Einstein branch, establishing a no-go theorem for this class of geometries.