Okay, here is the problem with that. Time itself doesn't have a direction. Our perception of it is directional. Quantum physics has done some interesting proofs on how what you do in the future affects what happened in the past. So the reality is that time isn't set and isn't directional. There are some interesting papers that theorize that all moments in time exist simultaneously. Oh and as for rivers only flowing in one direction, that also has exceptions. Often during earthquakes rivers are seen to reverse their flow. However, the flow reversal phenomenon in rivers is more commonly seen during extreme high tides. If I remember correctly, China has some that are world famous and happen like clockwork every year.
Einsteins equations used time as a dimension. He also intrinsically linked it to gravity. Hence the time dilation effects seen around heavy objects like planets and black holes. The fact that gravity affects time is demonstrated in the clocks on satellites. It isn't a huge difference, but it is a big enough one that it has to be taken into account for GPS satellites to work correctly.