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Stationary axially symmetric perturbations of a rotating black hole

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Abstract

A stationary axially symmetric perturbation of a rotating black hole due to a distribution of test matter is investigated. The Newman-Penrose spin coefficient formalism is used to derive a general set of equations describing the perturbed space-time. In a linear approximation we show that the mass and angular momentum of a rotating black hole is not affected by the perturbation. The metric perturbations near the horizon are given. We conclude that given a perturbing test fluid distribution, one can always find a corresponding metric perturbation such that the mass and angular momentum of the black hole are not changed. It was also noticed that when a → M, those perturbed spin coefficients and components of the Weyl tensor which determine the intrinsic properties of the incoming null cone near the horizon grow indefinitely.

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Authors and Affiliations

  1. California Institute of Technology, 91109, Pasadena, California

    Marek Demianski

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  1. Marek Demianski
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Supported in part by the National Science Foundation under grant No. GP-36687X.

On leave from the Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland.

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Demianski, M. Stationary axially symmetric perturbations of a rotating black hole. Gen Relat Gravit 7, 551–567 (1976). https://doi.org/10.1007/BF00763405

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