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

Nicolás Yunes and Frans Pretorius
Phys. Rev. D 79, 084043 – Published 30 April 2009

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 bound on the magnitude of the dynamical coupling constant of ξ1/4104km. More stringent bounds will require observations of inherently strong-field phenomena.

  • Received 26 February 2009

DOI:https://doi.org/10.1103/PhysRevD.79.084043

©2009 American Physical Society

Authors & Affiliations

Nicolás Yunes and Frans Pretorius

  • Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 79, Iss. 8 — 15 April 2009

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