  Black holes are a powerful setting for studying general relativity and
theories beyond GR. However, analytical solutions for rotating black holes in
beyond-GR theories are difficult to find because of the complexity of such
theories. In this paper, we solve for the deformation to the near-horizon
extremal Kerr metric due to two example string-inspired beyond-GR theories:
Einstein-dilaton-Gauss-Bonnet, and dynamical Chern-Simons theory. We accomplish
this by making use of the enhanced symmetry group of NHEK and the weak-coupling
limit of EdGB and dCS. We find that the EdGB metric deformation has a curvature
singularity, while the dCS metric is regular. From these solutions we compute
orbital frequencies, horizon areas, and entropies. This sets the stage for
analytically understanding the microscopic origin of black hole entropy in
beyond-GR theories.
