Generalized Einstein-Aether theories and the Solar System

It has been shown that generalized Einstein-Aether theories may lead to significant modifications to the nonrelativistic limit of the Einstein equations. In this paper we study the effect of a general class of such theories on the Solar System. We consider corrections to the gravitational potential in negative and positive powers of distance from the source. Using measurements of the perihelion shift of Mercury and time delay of radar signals to Cassini, we place constraints on these corrections. We find that a subclass of generalized Einstein-Aether theories is compatible with these constraints.

Figure 1

The metric fields $g_{tt}$ and $g_{rr}$ as functions of $r$, in the aether theory (solid line) and in general relativity (dotted line). We see that at the scale $r_m\simeq {10}^{15}\mathrm{km}$ the two models start to diverge. $r_{gm}\simeq {10}^{11}\mathrm{km}$ is the scale at which all growing corrections are expected to start to dominate.