Deformation of extremal black holes from stringy interactions

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.

Figure 1

The metric deformation functions $\delta v_1$ (solid) and $\delta v_2$ (dashed) as functions of $u$, for both dCS-deformed (red) and EdGB-deformed (blue) NHEK. Note that in ${\mathrm{D}}^2\mathrm{GB}$, $\delta v_1$ blows up at the two poles $u=\pm 1$.