According to GR, the future already exist?

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I'm afraid I don't understand what you mean by 'future exists'.
If you mean to ask whether future is predetermined, any deterministic theory will answer is in the affirmative.
Also, each observer experiences only his present in his frame of reference :-p ! Two observers mayn't agree on the temporal order of events,though.
 
no not really...but it does depend on what you mean. generally speaking relativity is a classical theory and is therefore deterministic, but what that means is also debatable.

you can see a diagram via SPECIAL RELATIVTY that shows the "future" via a light cone...

Or maybe you are thinking of determinism:

http://en.wikipedia.org/wiki/Determinism

which could mean that IF we knew every initial condition now then the future might be predetermined...but that conflicts directly with a lot quantum mechanics...
 
I'm not 100% on this, but I think the OP is more talking about whether general relativity allows time travel to the future ala science fiction (think Doc Brown going to see Marty's children).
 
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