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Would different observers agree on the age? Or is this question nonsensical? e.g. what's north of the north pole?

There are ways of estimating the ages of stellar bodies using various methods but is there a method for black holes?

My main stumbling block is the slowing down and 'stoppage' of time of objects near the event horizon as far as faraway observers are concerned. Theoretically one should be able to 'see' everything that 'fell' into the black hole since the time it (the EH) was formed. Obviously the older stuff should be more red-shifted than newer stuff but the entire spectrum should be seen: from slightly shifted to slightly less than infinitely shifted.

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When it comes to age what is the difference between a black hole or a star? The age depends on the choice of a time function, not on what signals can or cannot reach someone. –  MBN Apr 17 '14 at 11:46
I was going to suggest you simply ask the black hole how old it is, but then I remembered that black holes are kind of sensitive about their age.... and their weight; best not ask about either. –  ACuriousJim Apr 22 '14 at 13:28
On the positive side, I'd have to wait forever to get an answer back. –  BrianS May 16 '14 at 20:22

3 Answers 3

By black hole most of us mean the Schwarzschild metric, but the Schwarzschild metric is time independant i.e. it represents a black hole that has existed for ever and will continue to exist for ever. So it has no age in any useful sense of the word.

The problem with real black holes is that, as discussed at some length following Hawking's recent paper, Scwartzschild observers (i.e. you and I) will never see a true event horizon form. The best we will ever see is an apparent horizon. So if you consider a black hole to exist only if it has a true horizon then we can't assign an age to a black hole because none exist.

I'd probably go along with the pragmatic view expressed in BMS's answer. If you take the black hole at the centre of our galaxy it seems a bit pedantic to point out that it only possesses an apparent horizon, and therefore isn't really a black hole, when its worldline certainly leads to a black hole whether we'll be around to see it or not. Most of us would judge the age of the black hole to be about the age of the Milky Way.

Viewed this way, you're really asking about the age of the black hole's surroundings, whether it's a galaxy like the Milky Way or a supernova remnant as in BMS's example. You'd judge this age as you would for any similar cosmological body.

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If the black hole formation was accompanied by some type of explosion, say a supernova, you could estimate the age of the black hole by inspecting the properties of the supernova remnant. Here, you aren't looking at the black hole directly, but the stuff that was sent out at the time of its creation. This, method, coupled with knowledge of light-travel time to Earth, could yield the age of the black hole (from Earth).

There is a description how to estimate the age of supernova remnant on this NASA page (seems to be for kids, sorry).

If you want to follow up on such an object in our Milky Way, take a look at the WP page on the nebula W49B.

This answer does not address different observers, sorry.

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There are many problems currently with being able to age date a given black hole.

Firstly, the analogy of dating stars is not a good one. We date stars based upon their mass and spectral class, but this itself can be problematic, illustrated by the initial date of HD 140283 being older than that of the universe. This age was revised down, but it's still on the very edge even still. A black hole is not sustained by nuclear fusion, which follows a nice predictable chain all the way down to iron.

As mentioned above, if the black hole is sufficiently young, the nebula resulting from the supernova which created it. This problem with this is that these nebulae tend to dissipate after only a few million years. Because of this the window to date a black hole by this method is, in astronomical terms, quite narrow.

Black holes have been theorized to dissipate energy via Hawking radiation, a form of the Casimir effect. The problem with using this to date a black hole is that we have never detected it as yet (That I am aware of).

In short, the only way we can date a black hole is, fittingly, the only way we can locate them, i.e. by inference. These dates are not precise, and carry with them large error bars, and take into effect average density of stars and gas around them and how they differ from around the black hole, if the black hole is supermassive, the presence of an accretion disk / quasar, but all in all, there is no real way to date a black hole that we know of as of yet.

Sorry for the wall of text.

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