Yacine Ali-Haïmoud, Yanbei Chen
Chern-Simons (CS) modified gravity is an extension to general relativity (GR)
in which the metric is coupled to a scalar field, resulting in modified
Einstein field equations. In the dynamical theory, the scalar field is itself
sourced by the Pontryagin density of the space-time. In this paper, the coupled
system of equations for the metric and the scalar field is solved numerically
for slowly-rotating neutron stars described with realistic equations of state
and for slowly-rotating black holes. An analytic solution for a
constant-density nonrelativistic object is also presented. It is shown that the
black hole solution cannot be used to describe the exterior spacetime of a star
as was previously assumed. In addition, whereas previous analysis were limited
to the small-coupling regime, this paper considers arbitrarily large coupling
strengths. It is found that the CS modification leads to two effects on the
gravitomagnetic sector of the metric: (i) Near the surface of a star or the
horizon of a black hole, the magnitude of the gravitomagnetic potential is
decreased and frame-dragging effects are reduced in comparison to GR. (ii) In
the case of a star, the angular momentum J, as measured by distant observers,
is enhanced in CS gravity as compared to standard GR. For a large coupling
strength, the near-zone frame-dragging effects become significantly screened,
whereas the far-zone enhancement saturate at a maximum value max(Delta J) ~
(M/R) J. Using measurements of frame-dragging effects around the Earth by
Gravity Probe B and the LAGEOS satellites, a weak but robust constraint is set
to the characteristic CS lengthscale, xi^{1/4} <~ 10^8 km.
View original:
http://arxiv.org/abs/1110.5329
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