Nonlocal modification of the Kerr metric

TL;DR

This paper introduces a nonlocal modification to the Kerr metric using an infinite derivative approach, analyzing its effects on rotating black holes and horizon positions.

Contribution

It develops a novel nonlocal Kerr metric model by modifying the Laplace operator with an exponential operator, providing new insights into black hole properties.

Findings

Derived a nonlocal Kerr metric using infinite derivatives.

Numerically analyzed the shift in event horizon due to nonlocality.

Discussed properties of rotating black holes in the nonlocal model.

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 $g_{\mu\nu}=\eta_{\mu\nu}+\Phi l_{\mu}l_{\mu}$. 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 $\Phi$ 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 $\Phi$ 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.