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 $g_{\mu \nu }={\eta }_{\mu \nu }+\Phi l_{\mu }{l}_{\mu }$. Using Newman's approach we identify a shear free null congruence $\mathbf{l}$ 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 $△$ by its nonlocal version $\exp (-{\ell }^2△)△$. 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.

arXiv comment14 pages, 9 figures

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