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.

14 pages, 9 figures

References in corpus (11)

• Black holes and the double copy
• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Ultraviolet Complete Quantum Gravity
• Impulsive waves in ghost free infinite derivative gravity in anti-de Sitter spacetime
• Cosmological Solutions in Nonlocal Models
• Regular Rotating Black Holes: A Review
• Killing horizons and surface gravities for a well-behaved three-function generalisation of the Kerr spacetime
• A Newtonian analogue of Kerr black hole
• Non-local scalar fields in static spacetimes via heat kernels
• Infinite-derivative linearized gravity in convolutional form
• Regular black holes from higher-derivative effective delta sources

Cited by in corpus (5)

• Regular black holes inspired by quasi-topological gravity
• On effective models of regular black holes inspired by higher-derivative and nonlocal gravity
• Toward regular black holes in sixth-derivative gravity
• Scalar Quasinormal Modes of Rotating Regular Black Holes
• Dirac delta as a generalized holomorphic function