If you squeeze mass into a smaller and smaller volume (for instance when a big star collapses) the gravitational field around it gets stronger and stronger. At some point it becomes so strong that not even light can escape, and you have a black hole.
Until today, the understanding I had of black holes was as a spherical “event horizon” with a singularity at the centre. The event horizon is the surface of no return – anything which goes past it can never escape. The singularity is where quantum gravity kicks in, and is very handy for evading the speed-of-light limit in science fiction plots, where it functions as a gateway to a wormhole which can take the protagonists wherever they need to be.
All this changed during a talk by Samir Mathur of Ohio State University just now, here at the Lepton Photon meeting in Mumbai. It’s all to do with entropy.
Entropy is a measure of disorder, and it always increases. It is basically a count of how jumbled up something is. When you stir milk into a cup of tea you increase the entropy, because milk and tea mixed up constitute a more disordered state than when they are separate.
Think of it this way: the specific positions of every single molecule define a “microstate” of your cup of tea. There are hugely more microstates corresponding to a stirred cup of tea than there are to unmixed milk and tea. You can see this by imagining adding milk and tea molecules randomly to a cup one-by-one – it is hugely more likely that you end up with a mixed cup, rather than with all the milk in one place and the tea in another. So another way of thinking of entropy is as a count of the number of microstates corresponding to a particular physical system.
Black holes have entropy. They must do, since if you drop your cup of tea into a black hole, thermodynamics says its entropy cannot vanish. The entropy of the universe only increases. Jacob Bekenstein and Stephen Hawking showed the entropy of a black hole has to be proportional to the area of the event horizon shell around it. It gets bigger when you drop your cup of tea in.
But the idea of a black hole as a singularity surrounded by an event horizon doesn’t fit well with this. It’s basically a dot and a featureless shell. There’s only one microstate – dot in the middle, shell round the outside. Where is the entropy? Worse, when you drop a cup of tea in, the number of microstates doesn’t change. It’s still dot and shell. How does that work?
In Mathur’s calculations, the dot and shell picture is wrong. He has done calculations showing that at the event horizon of a black hole, the strings, membranes and all the other extradimensional stuff you get in string theory can be arranged in many different ways, giving many microstates, and thus providing the right amount of entropy. In this case, the weird quantum gravity stuff starts right at the event horizon, not at the dot in the middle. In fact there is no singularity at the middle any more. Tough luck on those space travellers, who will now have to go the long way round.
Mathur calls these things “fuzzballs”. They seem to solve the missing entropy problem. It’s not a completely new idea (Mathur first published it in 2002) but Mathur’s excellent talk was the first time I have come across it. It looks like it’s gaining ground as more details get worked out.
It’s difficult to do experiments with black holes (we don’t seem to be finding any at the LHC so far) but you can get quite a long way doing thought experiments.