How two observers on different gravitational fields would observe each other? As far as I know (from what I have heard) time passes differently (faster or slower) depending on the gravitational field of the observer (or an acceleration). So my question is, if an observer was about to use a telescope to observe someone in a different gravitational field, would he see him moving fast forward or in slow motion ??
(It seems a little bit confusing to me because I am thinking that if something like that is happening, and also if the man had the ability to manipulate gravity, then we could use a computer in space to solve time consuming problems and get the answer in time if we are in a very high gravitational field. It seems to me like a paradoxical way of things to work like that).
 A: I don't see it any more paradoxical than hibernating yourself until the calculation is complete.
If you have an event A in spacetime with coordinates $(t,r)$ and another event B with coordinates $(t',r')$, then the amount of time passed for an observer going from A to B would depend, in general, on his trajectory. You don't even need gravity for this, special theory of relativity tells you the same qualitative result - this is the main theme of twin paradox. In general relativity, the spacetime itself is curved, so the effect is even more interesting.
And to answer the question: usually, the time ticks slowly for observer in stronger gravitational field (the GR is more complicated for such simple claims to be made in general, actually I don't think it even makes sense for general spacetimes). This can be seen from Schwarzschild metric, which is a spacetime solution of spherically symmetric static source - so it is a good approximation to most of the objects in the universe. In such spacetime, the time of an observer sitting at constant position relative to a source as seen by an observer at infinity is given by the formula:
$$\Delta t'=\sqrt{1-\frac{r_s}{r}}\Delta t,$$ where $r_s$ is the Schwarzschild radius of the source, so for closer observer (which is in stronger gravitational field) the time ticks slower as seen by the observer that is further away (f.e. for an observer at $r=4r_s/3$ it would pass only 0.5s while for the distant observer it would 1s - as seen by the distant observer, so the distant observer would see the events at that distance to be 2 times slower).
