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

By N. Yunes, Frans Pretorius. 2009

234 citations recorded by the source corpus.

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 ${\ensuremath{\xi}}^{1/4}\ensuremath{\lesssim}{10}^{4}\text{ }\text{ }\mathrm{km}$. More stringent bounds will require observations of inherently strong-field phenomena.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6c749a7bb4db0c9e4f24cd458839ec287d2c8a50

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Citations in the corpus

Chern-Simons Modified General Relativity (2009, methodology): “Little is known about GW propagation or generation in dynamical CS modified gravity, although early efforts are being directed on that front [84,99].”
TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. II. BLACK HOLE IMAGES (2010, background): “…been suggested, which include naked singularities (Manko & Novikov 1992), exotic stellar objects (Friedberg, Lee, & Pang 1987; Mazur & Mottola 2001; Barceló et al. 2008), as well as a breakdown of general relativity itself on horizon scales (e.g., Yunes & Pretorius 2009; c.f. Psaltis et al. 2008).”
Testing black hole candidates with electromagnetic radiation (2015, methodology): “In this framework, non-rotating BHs are described by the Schwarzschild solution, but rotating BHs are different from those of Kerr (Yunes & Pretorius, 2009).”
Kerr black holes with Proca hair (2016, background): “g [35–42]); or 6) several of the above.”