# Leading higher-derivative corrections to Kerr geometry

## TL;DR

This paper derives the most general leading-order corrections to the Kerr black hole solution in theories with higher-derivative gravity terms, providing a series expansion for rotating black holes with large spin and analyzing their geometric properties.

## Contribution

It presents a unified framework for leading higher-derivative corrections to Kerr black holes, including several theories like Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons gravity, with detailed solutions and properties.

## Key findings

- Derived corrected Kerr metrics up to order $$ in spin parameter
- Provided a Mathematica notebook for arbitrary order calculations
- Analyzed horizon, ergosphere, light rings, and scalar hair modifications

## Abstract

We compute the most general leading-order correction to Kerr solution when the Einstein-Hilbert action is supplemented with higher-derivative terms, including the possibility of dynamical couplings controlled by scalars. The model we present depends on five parameters and it contains, as particular cases, Einstein-dilaton-Gauss-Bonnet gravity, dynamical Chern-Simons gravity and the effective action coming from Heterotic Superstring theory. By solving the corrected field equations, we find the modified Kerr metric that describes rotating black holes in these theories. We express the solution as a series in the spin parameter $\chi$, and we show that including enough terms in the expansion we are able to describe black holes with large spin. For the computations in the text we use an expansion up to order $\chi^{14}$, which is accurate for $\chi<0.7$, but we provide as well a Mathematica notebook that computes the solution at any given order. We study several properties of the corrected black holes, such as geometry of the horizon, ergosphere, light rings and scalar hair. Some of the corrections violate parity, and we highlight in those cases plots of horizons and ergospheres without $\mathbb{Z}_{2}$ symmetry.