Anyway, I was idly browsing physics.org and came upon the following piece: "Are there upper and lower limits to temperature?". Well, we all know the answer to that one - the coldest you can get is absolute zero. And then we get into zero-point energy and so on.

But how hot can you get? Temperature is particles zooming around, and if you have a bunch of particles getting faster and faster, then relativistically they're getting more and more massive. At some point, they will implode into a black hole and that must be the upper limit of temperature (see note below).

And then I thought, surely if you ran time backwards to the big bang, that's exactly what would happen - at some point in the early universe, the energy density would be so great the universe would implode into a black hole. So, running time the correct way again, if all the matter in the universe started in a black hole, how did it ever get out? Or do we live inside one?

Luckily, physicist John Baez has answered this question here. I will just quote an extract.

"

*Sometimes people find it hard to understand why the big bang is not a black hole. After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve space-time strongly. At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass. Nevertheless, the big bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly. How can this be?*

The short answer is that the big bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down. Space can be flat while space-time is not. The curvature can come from the temporal parts of the space-time metric which measures the deceleration of the expansion of the universe. So the total curvature of space-time is related to the density of matter but there is a contribution to curvature from the expansion as well as from any curvature of space. The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole. The Schwarzschild limit does not apply to rapidly expanding matter."

The short answer is that the big bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down. Space can be flat while space-time is not. The curvature can come from the temporal parts of the space-time metric which measures the deceleration of the expansion of the universe. So the total curvature of space-time is related to the density of matter but there is a contribution to curvature from the expansion as well as from any curvature of space. The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole. The Schwarzschild limit does not apply to rapidly expanding matter."

So there - worry over :-)

NOTE: Apparently even the idea that an object moving sufficiently rapidly will collapse into a black hole is wrong. Professor Baez explains that one here. See also "Does mass change with speed?".