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I've seen a lot of questions about maximum temperature and “absolute hot” — several ask if special relativity places any limits on temperature (clearly not). (Also this discussion of absolute hot on a NOVA blog post.)

But I haven't seen general relativity addressed in any of these discussions — shouldn't there be a point where increasing the temperature of a given system will cause it to exceed some critical threshold of energy density and consequently cause it to collapse into a black hole? And wouldn't that bound the upper limit of temperature?

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Yrast
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2 Answers2

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To continue Matas' comment: the definition of temperature is a quantity dependent on mean energy. It's sort of ugly when the particles all go near-relativistic, but there is no upper bound.

Interestingly, you can extend the definition to things like magnetic particle orientation states. In this case, beyond a certain magnetic field strength, all the particles are forced to align, and you get negative temperatures!

Carl Witthoft
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In principle yes, though the situation isn't as clear cut as you describe.

If you could confine a volume of matter within some volume then gradually heat it by adding energy to it then at some point the total energy density would exceed the density required to form a black hole and at that point the matter would start to collapse into a black hole.

However the density of a black hole depends on its size, so the maximum temperature would be dependent on the size of your assemblage of matter.

I suppose you could argue that the smallest volume measurable would be a Planck volume, and you could base your calculation on this. However at such fantastically high energy densities it isn't obvious that temperature has much meaning.

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John Rennie
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