Reflections in Cosmology 13: An Interesting Thought on Black Holes

One of the most astonishing consequences of Einstein’s general relativity has got to be its prediction of black holes. Though undetectable directly, the observational evidence is so compelling that astronomers no longer doubt their existence. In fact, we’re convinced that monster black holes reside in the centres of all large galaxies, including our own – and we often speak of them as if they are accepted fact.

An artist's impression of a black hole warping space and time in its vicinity, image courtesy of NASA

There’s an interesting thought experiment by Edward Harrison in his book that troubled me.

Let observer A fall into a black hole and observer B be far away in the outside world. B thinks, “Why should I worry about the fate of A? In my space and time, A is suspended forever in a frozen state and will never reach the singularity.” But is this true? Theory shows that in a closed universe of normal pressure and density there is only one future singularity. The observer in the collapsing star sees the outside world blueshifted, and the blueshift attains its extreme value when the star reaches the critical size and becomes a black hole. Everything in the outside world is seen speeded up by observer A, getting faster and faster as the collapse progresses, and, at the critical size, he sees that everything outisde happens with extreme rapidity (this is assuming that the observer has yet to be torn apart by tidal forces!). The future history of the universe passes in a flash. Suppose that in the far future, in tens or hundreds of billions of years in B’s time, the universe ceases to expand and collapses back into a second big bang (now believed to be highly unlikely after the discovery of dark energy and the accelerated expansion of the universe). The inside observer A sees all this happen in little or no time; the galaxies streak awayand then streak back again, and the outside world soars in density until it matches the density of the black hole. Time inside the black hole and time in the outside world now tick away together at the same rate, and A and B, holding hands, descend together into a cosmic singularity (assuming that B lives that long!). Observer B outside, who congratulates herself on not falling into the black hole, now finds herself on equal footing with the inside observer A, and together they meet their doom. ~ Edward Harrison, Cosmology: The Science of the Universe

But wait a minute here. If this is the case, will the core of a massive star ever collapse to form a singularity in the life-time of the universe, since, from the perspective of a distant observer, time in the vicinity of the collapsing core will have slowed almost to a halt? For a hypothetical observer in the collapsing core near the singularity, however, the entire history of the universe will whiz by in a flash. Does this mean that there will not be any singularities until the end of the universe – whatever that means? Will black holes ever form in the life-time of the Universe? Off the top of my head, I think that black holes do form in the lifetime of the universe – as long as all the matter collapses to within the Schwarzchild radius. However, the infalling matter will never arrive at the singularity within the life-time of the universe. I definitely need to consult someone who is more familiar with general relativity about this! There’s probably something wrong somewhere with my current understanding of black holes!

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