# Observing the age of the Universe when orbiting a black hole

Imagine a civilization developing on Planet X that is orbiting a black hole (or a similar gravitationally massive object). Given the time dilation near such a massive object, do the inhabitants of Planet X measure the age of the universe incorrectly? Does the universe appear much older for them?

As a follow-up question, is there a way to measure the age of the universe independently of the observer's circumstances? What about the extreme (and unlikely) case of a planet which is surrounded by black holes?

• Please check out how large the time dilation is (not that large). Any species that can calculate the age of the universe can also compensate in their calculations btw. And please be aware that this question doesn't make much sense since no life can exist on a planet orbiting a black hole. I think this is the much bigger plot hole here than if they calculate the age of the universe wrong. Priorities, people! – Raditz_35 May 19 '17 at 10:52
• "older" is a relative term. "Older" in relation to what or who? As to the followup: if you obscure the view of the universe then you have no way of measuring its age to any kind of accuracy. Our estimates of the age of the universe depend entirely on observation of the universe, in particular the cosmic microwave background radiation, and the expansion rate of the universe which is measured in the Doppler shift of faraway stars. – MichaelK May 19 '17 at 10:53
• I'm no expert on relativity, but I think the answer is that if the universe does appear much older for them, they're not necessarily measuring it incorrectly. Due to time dilation, the universe genuinely is much older (by other frames of reference) even though your observer's frame of reference is much "younger" in terms of the time that has passed. And you can't measure any passage of time independently of any observer's circumstances, because there is no central frame of reference for time or space, according to relativity – danl May 19 '17 at 10:53
• They would meassure the age of the universe in their own time units which are account for in their frame of reference. If we take into account the time dilation of their frame of reference when converting the units, it should would out. Afaict. – Theraot May 19 '17 at 11:03
• @MichaelK In what way is the view of the universe obscured in this example? – Raditz_35 May 19 '17 at 11:07

It is nearly impossible for a planet in orbit around a black hole to experience enough time dilation to make a significant difference in the age of the universe. This is because the innermost orbit around a nonrotating black hole is at 3x the event horizon radius, at which point the time dilation is $\sqrt{1-1/3^{2}}$=0.95. This is a difference of only 5% in the age of the universe.

You can do better using a near-maximally rotating black hole, which will allow orbits (in the rotation direction) almost down to the event horizon. This is how the black hole in Interstellar worked, but significant time dilation is still unlikely without a black hole above 99.999% of the maximum rotation. This is still ignoring tidal forces, which would probably destroy any planet trying to form within thousands of Schwartzchild radii of the black hole.

• This is an optimal answer for this question and I am completely with you, but I want to point out one thing: In fiction, usually a black hole almost completely stops time for a couple of light years and my guess is that only 3% of the general population have any problem with that. You seem to know some hard facts, let's keep it in the intentions of the poster I think and assume that the dilation was much larger. Do you know what would happen then? This isn't a question btw but a suggestion to make your answer even better – Raditz_35 May 19 '17 at 13:00
• Insert my rage about that planet in Interstellar (because you reminded me of it). How did they not do the math in reverse!? "He's been there for 10 years, we're going down. We'll be there an hour, that'll be 7 years for you." Helloooo, that means the dude's only been down there about 80 minutes! – Draco18s May 19 '17 at 14:44

There are some misconceptions both in the question and in the given answer.

There is no absolute time, every measurement changes according to the reference frame in which is taken. Therefore no one is right, no one is wrong. Nevertheless, our estimate of the age of the universe comes from the lambda-CDM model of cosmology, in which the metric of the universe is the FRLW metric, that is an expanding universe. A black hole is still only a local disturbance, compared to the expansion of the universe, so even near a black hole one should use the FRLW metric and the age of the universe would be the same.

If, hypothetically the black hole is non negligible compared to the expansion of the universe, one could probably makes some estimates from a de Sitter–Schwarzschild metric, even though I've never seen such a calculation.

Ever seen the movie interstellar?