# Uncertainty principle within a neutron star or black hole

Take the time-energy uncertainty relation, $\Delta$$E$$\Delta$$T$$\ge$$\hbar/2$.

My question is based on my confusion about the effect this relation may have within the interior of a highly compressed object such as a neutron star:

Would it:

• provide a source of repulsive energy, albeit over a very short time span?
• or would it actually represent effective mass, increasing the inward directed gravitational force?
• or would it average out as in the flatspace metric, producing no overall effect?

My background is at beginner GR level, but I do appreciate that this relation can have a large effect at very short scales, I'm just not sure if these are relevant, even within a highly compressed object such as a neutron star, although a black hole is a different matter.

EDIT: I have posted an answer myself below.

• Obligatory reading: This question and its answers. $\Delta t$ is probably not what you think it is, and this uncertainty relation probably doesn't mean what you think it does. – ACuriousMind May 21 '15 at 12:15
• @ACuriousMind thank you very much for that advice. I had started reading a John Baez article based around the fact that time is not an operator (and the consequences of that for the above relation) and I will approach it again with that in mind. – user81619 May 21 '15 at 12:35