Is general relativity compatible with an arrow of time?

Question

The spacetime of Special Relativity is Minkowski's "Block Universe" where time is treated as a dimension. Does General Relativity allow for an arrow of time or "flow" of time? If yes, can this be considered the cosmological arrow of time in the expanding universe, since the Friedmann equations are derived from Einstein's Field Equations?

Answer 1

General Relativity, on its own, does not say anything about the arrow of time. It is possible to conceive of a spacetime where an arrow of time cannot be self-consistently defined. Such spacetimes are called non-time-orientable; the easiest example to conceive of (if a rather artificial one) is obtained by taking a “strip” of Minkowski spacetime and gluing the ends together with a half-twist, like a Möbius strip.

It is generally assumed that spacetimes that are “physically reasonable”, though, are time-orientable. However, all this means is that there is a self-consistent notion of “past” and “future” throughout the spacetime; it does not actually distinguish between these two notions.