I was wondering what the temperature beyond the event horizon of a black hole might be, would the compression of matter towards the singularity heat material up to a level comparable to the Planck temperature, or would the gravitational forces restrict all vibration, even down to the quantum level?

 

Which lead me to thinking, if that was the case, would a singularity have any zero-point energy, or would the singulariy violate Heisenberg's uncertainty principle?

There are several ways to define temperature, such as molecular/atomic motion, or radiating spectrum.

None of them are readily applicable to the 'interior' of the event horizon.

 

The surface area of the event horizon can, however, be related to the entropy of a BH, and by extension, its temperature.