Leading effective field theory corrections to the Kerr metric at all spins

Abstract

The leading corrections to General Relativity can be parametrized by higher-derivative interactions in a low-energy effective field theory, in a way that is general and agnostic to the precise UV completion of gravity. Using pseudospectral methods, we compute the leading-order corrections to the Kerr metric across the entire range of sub-extremal values of spin and analyse their impact on physical quantities. We find that near-extremal black holes are most affected by the higher-derivative corrections, making them especially sensitive probes of new physics. A dataset of solutions and the code used to produce them are publicly available.

Figures (2)

• Figure 1: Absolute difference between the numerical and analytic values of $\kappa_{(4)}$ (top) and $\Omega_{H,(4)}$ (bottom) for both parity sectors. The numerical values were obtained using resolutions $(N_x, N_y) = (50,16)$ for $a/M < 0.65$, $(N_x, N_y) = (60,24)$ for $0.65 \leq a/M < 0.999$, and $(N_x, N_y) = (64,28)$ for $a/M = 0.999$. In the parity-odd case, the analytic values of these quantities are identically zero.
• Figure 2: Corrections to the perimetral location (top) and orbital frequency at the light ring (bottom) for spin values up to $a/M=0.99$.