A partial Cauchy surface must be compact if its future Cauchy horizon is compact (independent of field equations and energy conditions).

The most widely discussed chronology protection theorem/no-go result for time machines in the context of classical general relativity theory is due to Hawking (1992a). Before stating the result, note first that, independently of the Einstein field equations and energy conditions, a partial Cauchy surface \(\Sigma\) must be compact if its future Cauchy horizon \(H^+ (\Sigma)\) is compact (see Hawking 1992a and Chrusciel and Isenberg 1993). However, it is geometrically allowed that \(\Sigma\