Classical Gravity Does Not Refract Negatively

We appraise recent claims that classical gravitation can induce negative refraction of electromagnetic radiation in vacuum. By recasting the previous literature in covariant notation, we show that the criterion used hitherto for determining negative refraction in vacuum is inappropriate, and can even be satisfied by parametrized transformations in Minkowski spacetime. Using instead a covariantly acceptable definition, we find that in classical vacuum the power flux of a plane electromagnetic wave points in the direction of phase advance.

Figure 1

Forward and backward propagating waves in Minkowski spacetime. In ($\overline{t}$, $\overline{z}$) coordinates the wave vectors (broken arrows) have components $K_{\pm }^{\overline{\mu }}=(\omega ,\pm \omega )$. In ($t=\overline{t}-a\overline{z}$, $z=\overline{z}$) coordinates, the same wave vectors have components $K_{\pm }^{\mu }=\mathbf{(}\omega (1\mp a),\pm \omega \mathbf{)}$ [c.f. Eq. (7)].