Theories of Gravity with Structure-Dependentγ's

A gauge theory for the Lorentz connection of a space-time describes geometries of stars with variable parametrized post-Newtonian parameter $\gamma$; its value depends explicitly on the structure of a star: The value of $\gamma$ for a neutron star is different from that for the solar system ($\left|{{\gamma }_{\odot }}^{-1\mathrm{}}\right|<~{10}^{-2\mathrm{}}$). Because of the absence of a "local parity invariance" $\gamma$ is positive for ordinary stars and $\gamma$ is negative for sources of gravity consisting of antimatter.