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Systematic study of event horizons and pathologies of parametrically deformed Kerr spacetimes

Tim Johannsen

  • Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada
  • Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • Physics Department, University of Arizona, Tucson, Arizona 85721, USA

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Phys. Rev. D 87, 124017 – Published 17 June, 2013

DOI: https://doi.org/10.1103/PhysRevD.87.124017

Abstract

In general relativity, all black holes in vacuum are described by the Kerr metric, which has only two independent parameters: the mass and the spin. The unique dependence on these two parameters is known as the “no-hair” theorem. This theorem may be tested observationally by using electromagnetic or gravitational-wave observations to map the spacetime around a candidate black hole and measure potential deviations from the Kerr metric. Several parametric frameworks have been constructed for tests of the no-hair theorem. Due to the uniqueness of the Kerr metric, any such parametric framework must violate at least one of the assumptions of the no-hair theorem. This can lead to pathologies in the spacetime, such as closed timelike curves or singularities, which may hamper using the metric in the strong-field regime. In this paper, I analyze in detail several parametric frameworks and show explicitly the manner in which they differ from the Kerr metric. I calculate the coordinate locations of event horizons in these metrics, if any exist, using methods adapted from the numerical relativity literature. I identify the regions where each parametric deviation is unphysical as well as the range of coordinates and parameters for which each spacetime remains a regular extension of the Kerr metric and is, therefore, suitable for observational tests of the no-hair theorem.

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Information

Phys. Rev. D 87, 124017– Published 17 June, 2013
  • Received 29 April 2013
Article part of CHORUS

© 2013 American Physical Society

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