Light-bending tests of Lorentz invariance

Classical light-bending is investigated for weak gravitational fields in the presence of hypothetical local Lorentz violation. Using an effective field theory framework that describes general deviations from local Lorentz invariance, we derive a modified deflection angle for light passing near a massive body. The results include anisotropic effects not present for spherical sources in General Relativity as well as Weak Equivalence Principle violation. We develop an expression for the relative deflection of two distant stars that can be used to analyze data in past and future solar-system observations. The measurement sensitivities of such tests to coefficients for Lorentz violation are discussed.

Figure 1

The basic light-bending scenario. The vector ${\overrightarrow{r}}_p$ extends from the central body $L$ to the observer, ${\overrightarrow{r}}_e$ is the vector from the central body to the emitter, $\widehat{n}$ is in the direction of the unperturbed path, and $\overrightarrow{b}$ is the impact parameter vector (perpendicular to $\widehat{n}$).

Figure 2

Initial uniform star field (left). Apparent shift of distant light in the standard general relativity case (right).

Figure 3

Anisotropic apparent shift of star field due to the ${\overline{s}}_{xx}-{\overline{s}}_{yy}$ coefficients (left) and the ${\overline{s}}_{xy}$ coefficients (right). The local $x$ coordinate runs horizontally and $y$ is vertical.

Figure 4

Solar light-bending scenario in the presence of a reference source. For the source and reference star, we have the impact parameters $\overrightarrow{b}$ and ${\overrightarrow{b}}_r$, and directions $\widehat{n}$ and ${\widehat{n}}_r$, respectively. The reference plane shown is that spanned by $\overrightarrow{b}$ and ${\overrightarrow{b}}_r$.

Figure 5

The behavior of the deflection $\delta \Psi$ near-conjunction plotted as function of time $t$ around the summer solstice as the Sun moves across the field of view. The solid curve is the deflection from GR, the dashed curve is the deflection amplitude from the coefficients ${\overline{s}}_A$, and the dotted curve is the deflection amplitude from the coefficients ${\overline{s}}_B$.