Nonlocal modification of the Kerr metric

Abstract

In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr-Schild form of the Kerr metric $g_{μν}=η_{μν}+Φl_μl_μ$. Using Newman's approach we identify a shear free null congruence $\boldsymbol{l}$ with the generators of the null cone with apex at a point $p$ in the complex space. The Kerr metric is obtained if the potential $Φ$ is chosen to be a solution of the flat Laplace equation for a point source at the apex $p$. To construct the nonlocal modification of the Kerr metric we modify the Laplace operator $\triangle$ by its nonlocal version $\exp(-\ell^2\triangle)\triangle$. We found the potential $Φ$ in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality.