CPT and relativity

with earlier CQWs and the idea that in relativity there’s no fundamental difference between space and time coordinates (apart from the signature of the metric), could you formulate a combined \(PT\)-invariance of the field equation, where \(\vec{x}\rightarrow-\vec{x}\) and \(t\rightarrow-t\)? what’s the relation to charges of the gravitational field (i.e. masses) and a combined \(CPT\)-symmetry?