| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>g</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>=</mo><msub><mi>η</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>+</mo><mo>Φ</mo><msub><mi>l</mi><mi>μ</mi></msub><msub><mi>l</mi><mi>μ</mi></msub></mrow></semantics></math></inline-formula>. Using Newman’s approach, we identify a shear free null congruence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">l</mi></semantics></math></inline-formula> with the generators of the null cone with apex at a point <i>p</i> in the complex space. The Kerr metric is obtained if the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula> is chosen to be a solution of the flat Laplace equation for a point source at the apex <i>p</i>. To construct the nonlocal modification of the Kerr metric, we modify the Laplace operator <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>▵</mo></mrow></semantics></math> by its nonlocal version <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">exp</mo><mo>(</mo><mo>−</mo><msup><mo>ℓ</mo><mn>2</mn></msup><mo>▵</mo><mo>)</mo><mo>▵</mo></mrow></semantics></math></inline-formula>. We found the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula> 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. AlbertaThy 5–23.
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