Analytic and accurate approximate metrics for black holes with arbitrary rotation in beyond-Einstein gravity using spectral methods

Testing general relativity in the strong-field regime demands precise predictions from modified gravity. Such predictions hinge on obtaining accurate spacetime metrics for black holes beyond Einstein's theory, especially in the rapidly spinning regime where deviations can be large. In this talk, I will present a general and efficient framework, based on spectral and pseudospectral methods, to compute analytic, approximate metrics for stationary, axisymmetric black holes in broad classes of effective-field-theory extensions of general relativity. By recasting the modified Einstein equations into a compact system of algebraic relations, the framework enables fast and high-precision solutions using standard linear algebra tools. I will illustrate this method in dynamical Chern–Simons gravity, scalar Gauss–Bonnet gravity, and axidilaton gravity, producing metric and scalar-field configurations valid for spins up to 0.999 and accurate to better than one part in one hundred million. I will conclude by exploring how key physical observables are altered in this high-spin regime, identifying rapidly rotating black holes as powerful laboratories for testing the foundations of general relativity.