Erratum to: 'Maxwell–Chern–Simons theory for curved spacetime backgrounds' [Nucl. Phys. B 731 (2005) 125–139]

(1) ( kμk μ )2 +mkμkζνζ ν −m2(ζμkμ)2 = 0, where kμ ≡ (ω/c, k) is the wave number four-vector, m the CS mass scale, and ζμ = ζμ(x) the spacelike CS “four-vector”. The geometrical-optics approximation of this theory was considered and a modified wave number four-vector k was introduced. It was claimed, in Section 3 of Ref. [1], that this k obeys a geodesic-like equation. However, we have now realized that this statement is incorrect. Instead of Eq. (3.9) of Ref. [1], the complete equation for k reads