It's unclear what exactly you have in mind, but the equations of GR simply predict that the topology of space-time is not that of R^4, but includes boundaries at finite (temporal) distance, so-called space-like singularities [1]. This is not unusual. For example, the solutions to the ODE dx/dt = -1/x topologically live on the half line.

[1] https://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singul...