Neutron stars are sensitive laboratories for testing general relativity , especially when considering deviations where velocities are relativistic and gravitational fields are strong .
One such deviation is described by dynamical , Chern-Simons modified gravity , where the Einstein-Hilbert action is modified through the addition of the gravitational parity-violating Pontryagin density coupled to a field .
This four-dimensional effective theory arises naturally both in perturbative and non-perturbative string theory , loop quantum gravity , and generic effective field theory expansions .
We calculate here Chern-Simons modifications to the properties and gravitational fields of slowly spinning neutron stars .
We find that the Chern-Simons correction affects only the gravitomagnetic sector of the metric to leading order , thus introducing modifications to the moment of inertia but not to the mass-radius relation .
We show that an observational determination of the moment of inertia to an accuracy of 10 \% , as is expected from near-future observations of the double pulsar , will place a constraint on the Chern-Simons coupling constant of \xi ^ { 1 / 4 } \lesssim 5 { km } , which is at least three-orders of magnitude stronger than the previous strongest bound .