Veracity of a Singularity
So, in the last article we discussed some desperate approaches to debunk the idea of the Big Bang and we witnessed how those theories came crushing down into pieces one by one as the observations were made and finally, we came to a conclusion that there was a bang IF the general theory of relativity was correct.
So the question now is: Does general relativity predict the beginning of time? The answer to this was provided by a British physicist, Roger Penrose, in 1965. Before we move on to what he did I think it’s better to introduce and define some terms which are very crucial to understand The Penrose Theorem and how it leads us to general relativity and the origin of our universe. I’m not going to save the best part for the last so first of all, SINGULARITY- the most fascinating word and one of the proofs of Penrose’s work in itself, singularity means a point of infinite density/ gravitational field or where the curvature of space-time becomes infinite, at these extreme physical conditions everything that you know, all the laws governing physics and math they all simply vanish, it’s the absolute no man’s land where everything including time, matter, and space itself would annihilate. Another interesting physical feature is a LIGHT CONE, in special and general relativity a light cone is a path that a flash of light takes, originating from a single event (single point in space and a single moment in time) and travelling in all directions would take in as space-time progresses. To read more about it, click here.
The next thing on the menu is the EVENT HORIZON, in the vicinity of compact massive objects the gravity is so strong that even light cannot escape from it, it is the boundary across which everything is doomed to fall inwards towards a central point which is of course singularity. The definition of the event horizon looks simple however the idea behind that is much trickier, we can all accept the idea of light coming from outside converging towards a focal point due to the gravitational field (gravitational lensing) but the interesting thing inside the black hole is that any light inside would also try to converge (and not diverge outwards). So, the definition would change according to your position with reference to the black hole, Penrose, however, came up with a much more precise idea- the trapped surface that is that any surface which has the property that the null geodesics (path travelled by light in free fall in a gravitational field) pointed outwards from the surface would fall actually downward. Any surface inside a black hole is a trapped surface.
Now let’s come back to the main part of our discussion, in 1939, Robert Oppenheimer and Hartland Snyder showed that a perfectly sphere and perfectly smooth ball of dust could collapse into a Schwarzschild black hole- into a singularity which means that if there were even a slightest divergence from perfectly sphere symmetry the particles falling inwards won’t meet at a common center and this infalling matter would instead fly back outwards in an explosion; this idea was challenged by Penrose who very cleverly showed that singularities were unavoidable in general relativity and that any distribution of normal matter, no matter how messy, would have an event horizon and a singularity provided that it is compacted to a very small volume in space. He showed that according to Einstein’s theory and some assumptions black holes must contain singularities regardless of the nature of their formation. He did that by showing that the geodesics of space time come to an end inside a black hole. Null geodesics travelling into or past any gravitational field tend to converge and be focused- the phenomenon which we call as gravitational lensing. Now the interesting thing he showed was that some of the parallel null geodesics leaving any trapped surface (going either up or down) had to converge, cross each other and come to a focus, and that they would not behave as null geodesics beyond the focal point they would terminate inside the black hole and at a focal point- this phenomenon is referred to as geodesic incompleteness, because these geodesics are used to map space and time, geodesic incompleteness would mean that space-time would end at these focal points, they would literally cease at this point. Prior to Penrose it was believed that all of space-time was smooth and could be traced indefinitely into past and future cleanly defined anywhere; Penrose showed that space and time could have holes with infinite curvature- infinite gravity (or singularities). This work of his came to be known as singularity theorem. However, Penrose didn’t show what kind of singularities would form inside a black hole, he only showed that these were inevitable. In a Schwarzschild black hole, time ceases at a point-like central singularity; while in a Kerr black hole space ends at the ring singularity. Right after Penrose published his paper, a young research student was inspired by his ideas and wanted to extend it to a much greater level – the ideas about the universe, the student was none other than Stephen Hawking, what Hawking did was reverse the time in Penrose’s theorem so that the collapse became an expansion, the conditions of his theorem were still valid, provided that the universe were roughly like a Friedmann model on large scales at the present time.
We now know that Penrose’s theorem stated that any star would end in a singularity; the time reversed argument stated that any Friedmann-like expanding universe must have begun with a singularity. I think we should take at least a minute to realize how beautifully the concept of Big Bang is being gratified without violating any limitations or laws. Penrose’s theorem required that the universe be infinite in space so Hawking used it to prove that there should be a singularity ONLY IF the universe was expanding fast enough to avoid collapsing again, because only that Friedmann model was infinite in space. In 1970 Penrose and Hawking published a joint paper, in which they removed all technical conditions for the theorem and developed new mathematical technique to prove that there must have been a Big Bang singularity provided only that general relativity was a valid theory and that the universe contains as much matter as we observe. So it is now generally accepted that the universe did have a beginning.
We shall meet again next month with another interesting article, till then keep the mind bulbs on.
- Muhammad Umair Ansari
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