Fig. 1

General relativistic engineering of causal relations between space-time events using a massive body. Initially synchronised clocks a and b are positioned at fixed distances from a far-away agent whose time coordinate is t. Event A (B) is defined by the clock of a (b) showing proper time τ^*. In configuration \({\mathrm{K}}_{{\mathrm{A}} \prec {\mathrm{B}}}\) (left) a mass is placed closer to b than to a. Due to gravitational time dilation, event A can end up in the causal past of event B: for a sufficiently large τ^* the time difference between the clocks becomes greater than it takes light to travel between them. Light emitted at event A reaches clock b before the event B occurs. Configuration \({\mathrm{K}}_{{\mathrm{B}} \prec {\mathrm{A}}}\) (right) is fully analogous to \({\mathrm{K}}_{{\mathrm{A}} \prec {\mathrm{B}}}\): the mass is placed closer to clock a and the event B can end up in the causal past of the event A