Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation

Yunes, Nicolas; Pretorius, Frans

doi:10.1103/PHYSREVD.79.084043

Title: Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation

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Abstract

The low-energy limit of string theory contains an anomaly-canceling correction to the Einstein-Hilbert action, which defines an effective theory: Chern-Simons (CS) modified gravity. The CS correction consists of the product of a scalar field with the Pontryagin density, where the former can be treated as a background field (nondynamical formulation) or as an evolving field (dynamical formulation). Many solutions of general relativity persist in the modified theory; a notable exception is the Kerr metric, which has sparked a search for rotating black hole solutions. Here, for the first time, we find a solution describing a rotating black hole within the dynamical framework, and in the small-coupling/slow-rotation limit. The solution is axisymmetric and stationary, constituting a deformation of the Kerr metric with dipole scalar 'hair', whose effect on geodesic motion is to weaken the frame-dragging effect and shift the location of the innermost stable circular orbit outwards (inwards) relative to Kerr for corotating (counterrotating) geodesics. We further show that the correction to the metric scales inversely with the fourth power of the radial distance to the black hole, suggesting it will escape any meaningful bounds from weak-field experiments. For example, using binary pulsar data we can only place an initial boundmore »« less

Authors:

Yunes, Nicolas; Pretorius, Frans ^[1]

Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)

Publication Date:: Wed Apr 15 00:00:00 EDT 2009

OSTI Identifier:: 21308337

Resource Type:: Journal Article

Journal Name:: Physical Review. D, Particles Fields

Additional Journal Information:: Journal Volume: 79; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.79.084043; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; AXIAL SYMMETRY; BLACK HOLES; CORRECTIONS; COUPLING; COUPLING CONSTANTS; DISTANCE; EXCEPTIONS; GENERAL RELATIVITY THEORY; GRAVITATION; HILBERT SPACE; KERR METRIC; MATHEMATICAL SOLUTIONS; PULSARS; SCALAR FIELDS; STRING MODELS; STRING THEORY

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                    Yunes, Nicolas, and Pretorius, Frans. Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation.  United States: N. p., 2009. 
        Web.  doi:10.1103/PHYSREVD.79.084043.

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                    Yunes, Nicolas, & Pretorius, Frans. Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation.  United States.  https://doi.org/10.1103/PHYSREVD.79.084043

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                    Yunes, Nicolas, and Pretorius, Frans. 2009.  
        "Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation".  United States.  https://doi.org/10.1103/PHYSREVD.79.084043.

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@article{osti_21308337,

  title        = {Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation},

  author       = {Yunes, Nicolas and Pretorius, Frans},

  abstractNote = {The low-energy limit of string theory contains an anomaly-canceling correction to the Einstein-Hilbert action, which defines an effective theory: Chern-Simons (CS) modified gravity. The CS correction consists of the product of a scalar field with the Pontryagin density, where the former can be treated as a background field (nondynamical formulation) or as an evolving field (dynamical formulation). Many solutions of general relativity persist in the modified theory; a notable exception is the Kerr metric, which has sparked a search for rotating black hole solutions. Here, for the first time, we find a solution describing a rotating black hole within the dynamical framework, and in the small-coupling/slow-rotation limit. The solution is axisymmetric and stationary, constituting a deformation of the Kerr metric with dipole scalar 'hair', whose effect on geodesic motion is to weaken the frame-dragging effect and shift the location of the innermost stable circular orbit outwards (inwards) relative to Kerr for corotating (counterrotating) geodesics. We further show that the correction to the metric scales inversely with the fourth power of the radial distance to the black hole, suggesting it will escape any meaningful bounds from weak-field experiments. For example, using binary pulsar data we can only place an initial bound on the magnitude of the dynamical coupling constant of {xi}{sup 1/4} < or approx. 10{sup 4} km. More stringent bounds will require observations of inherently strong-field phenomena.},

  doi          = {10.1103/PHYSREVD.79.084043},

  url          = {https://www.osti.gov/biblio/21308337},
  journal      = {Physical Review. D, Particles Fields},

  issn         = {0556-2821},

  number       = 8,

  volume       = 79,

  place        = {United States},

  year         = {Wed Apr 15 00:00:00 EDT 2009},

  month        = {Wed Apr 15 00:00:00 EDT 2009}

}

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