  The deletion of the points  \(p_1\)–\(p_4\) means that the  Deutsch-Politzer spacetime is singular in the sense that it is  geodesically   incomplete.[16]  It would be too drastic to require of a time-machine hosting  spacetime that it be geodesically complete. And in any case the  offending feature of Deutsch-Politzer can be gotten rid of by the  following trick. Multiplying the flat Lorentzian metric  \(\eta_{ab}\) of Deutsch-Politzer spacetime by a scalar function \(j(x, t) \gt\) produces a new  metric \(\eta '_{ab} :=\) j  \(\eta_{ab}\) which is conformal to the original metric  and, thus, has exactly the same causal features as the original  metric. But if the conformal factor \(j\) is chosen to  “blow up” as the missing points  \(p_1\)–\(p_4\) are approached,  the resulting spacetime is geodesically complete—intuitively,  the singularities have been pushed off to infinity.