Slowly Rotating Black Holes in Dynamical Chern-Simons Gravity:
  Deformation Quadratic in the Spin
  We derive a stationary and axisymmetric black hole solution to quadratic
order in the spin angular momentum. The previously found, linear-in-spin terms
modify the odd-parity sector of the metric, while the new corrections appear in
the even-parity sector. These corrections modify the quadrupole moment, as well
as the (coordinate-dependent) location of the event horizon and the ergoregion.
Although the linear-in-spin metric is of Petrov type D, the quadratic order
terms render it of type I. The metric does not possess a second-order Killing
tensor or a Carter-like constant. The new metric does not possess closed
timelike curves or spacetime regions that violate causality outside of the
event horizon. The new, even-parity modifications to the Kerr metric decay less
rapidly at spatial infinity than the leading-order in spin, odd-parity ones,
and thus, the former are more important when considering black holes that are
rotating moderately fast. We calculate the modifications to the Hamiltonian,
binding energy and Kepler's third law. These modifications are crucial for the
construction of gravitational wave templates for black hole binaries, which
will enter at second post-Newtonian order, just like dissipative modifications
found previously.
