Effects of Chern-Simons gravity on bodies orbiting the Earth

One of the possible low-energy consequences of string theory is the addition of a Chern-Simons term to the standard Einstein-Hilbert action of general relativity. It can be argued that the quintessence field should couple to this Chern-Simons term, and if so, it drives in the linearized theory a parity-violating interaction between the gravito-electric and gravitomagnetic fields. In this paper, the linearized spacetime for Chern-Simons gravity around a massive spinning body is found to include new modifications to the gravitomagnetic field that have not appeared in previous work. The orbits of test bodies and the precession of gyroscopes in this spacetime are calculated, leading to new constraints on the Chern-Simons parameter space due to current satellite experiments.

Figure 1

The ratio ${\dot{\Omega }}_{\mathrm{CS}}/{\dot{\Omega }}_{\mathrm{GR}}$ for the LAGEOS satellites orbiting with a semimajor axis of $a\approx 12000\mathrm{km}$. A 10% verification of general relativity [16] (the shaded region) leads to a lower limit on the Chern-Simons mass of $|m_{\mathrm{cs}}|\gtrsim 0.001{\mathrm{km}}^{-1}$. A 1% verification of the Lense-Thirring drag will improve this bound on $m_{\mathrm{cs}}$ by a factor of roughly five.

Figure 2

The ratio ${\dot{\Phi }}_{\mathrm{CS}}/{\dot{\Phi }}_{\mathrm{GR}}$ for Gravity Probe B in a polar orbit at an altitude of approximately 640 km. A 10% verification of general relativity (the shaded region) leads to a lower limit on the Chern-Simons mass of $|m_{\mathrm{cs}}|\gtrsim 0.01{\mathrm{km}}^{-1}$, an order of magnitude improvement over the LAGEOS result.