Intuitively - why aren't black holes hot?

Chronos

Given that events occuring inside the event horizon are entirely unobservable, is there a point to this line of discussion?

enosis_

No, it seems a bit redundant. The fascinating thing for me - related to the discussion of temperature - is what happens to the heat/energy as it is consumed into the singularity?

justsomeguy

The textbook answer is that it's "simply" converted to mass. Keep in mind the singularity isn't a "thing", it's just a word to describe a place where the calculations provided by the theory no longer work.

enosis_

Perhaps the better question might be is this the original state of the converted energy - or a step closer to it?

codex34

Any theory for gravity based on non scalar mathematics fails at the point of inflection, which is exactly why the author of relativity objected to theories referencing points within the mass radius, once you remove the mass radius from calculations you return to non scalar mathematics, a realm in which only wizards and trolls reside.

Singularities are the problems with mathematical philosophy that physics fails to notice.

Chronos

Mathematics is the language of physics. Yes, there are mathematical illusions and situations where our models fail to include, or, properly parameterize all of the relevant variables. But, I disagree there is anything philosphical about mathematics.

codex34

So what exactly is differentiation? or infinity? :)
What happens at points of inflection?, what does a change in sign mean?, and how does it apply to any given model?
Black hole theory is a primary candidate for study, objects accelerate to a near complete halt in a very short time below the point of inflection, which is opposite to what an object does above the point of inflection.
The change in sign has no real meaning in mathematics?
Gravitational models would still work if we ignore the maths below the point of inflection, however would they still work if we ignored the maths above the point of inflection?

Mathematics is a shorthand for ideas expressed in natural languages, the language of physics is natural language, sometimes expressed in shorthand form.

Chronos

Differentiation is mathematically rigorous way of expressing an ordered change. The proper way to treat an event horizon is as an indefinite integral. You can't differentiate an indefinite integral in the way you are suggesting.