Signals for Lorentz violation in post-Newtonian gravity

The pure-gravity sector of the minimal standard-model extension is studied in the limit of Riemann spacetime. A method is developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the Minkowski vacuum, while allowing for the dynamics of the 20 independent coefficients for Lorentz violation. The linearized effective equations are solved to obtain the post-Newtonian metric. The corresponding post-Newtonian behavior of a perfect fluid is studied and applied to the gravitating many-body system. Illustrative examples of the methodology are provided using bumblebee models. The implications of the general theoretical results are studied for a variety of existing and proposed gravitational experiments, including lunar and satellite laser-ranging, laboratory experiments with gravimeters and torsion pendula, measurements of the spin precession of orbiting gyroscopes, timing studies of signals from binary pulsars, and the classic tests involving the perihelion precession and the time delay of light. For each type of experiment considered, estimates of the attainable sensitivities are provided. Numerous effects of local Lorentz violation can be studied in existing or near-future experiments at sensitivities ranging from parts in ${10}^4$ down to parts in ${10}^{15}$.

Figure 1

Schematic relationship between the pure-gravity sector of the minimal SME and the PPN formalism.

Figure 2

Sun-centered celestial-equatorial frame.

Figure 3

The Earth-satellite system in the Sun-centered frame.

Figure 4

Satellite orbital parameters in the Sun-centered frame. For simplicity, the Earth is shown as if it were translated to the origin of the Sun-centered coordinates.

Figure 5

Idealized apparatus with $N=3$ masses.

Figure 6

Definitions for the elliptical orbit.

Figure 7

Elliptical orbits in the post-Newtonian frame of the binary pulsar.