The accepted age of the Universe is 13 billion years give or take. If you were a super space being and hypothetically had spent a large portion of this time sitting next to a black hole then your experience of time, in fact time itself, 'runs' at a slower pace at your location. Does this mean that at this point the Universe is younger? Is the conventional age of the Universe calculated assuming no effects of general relativity on the time calculation? Or am I completely deluded? Any related insight would be great also. Cheers
No, the age of the universe doesn't depend on the observer. What depends on the observer is the "perceived" time that has passed since the Big Bang.
What you are asking is if the conformal time and the age of the universe are the same and the answer is negative as you can see in that link.