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LostConjugate
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Is there agreement here or are all/most of the neutrons in the same state?
Yes, there must certainly be a quantum state associated to a black hole in a quantum theory of gravity. This quantum state is just not suitably defined using the observables you refer to.LostConjugate said:So there is no quantum state for a black hole?
humanino said:The concept of degeneracy pressure is useful to describe slow processes of collapse for moderate size stars. This degeneracy can never be overcome. Ever more energy must be put into the system to excite the fermions into higher momenta, until so much energy is stored that the BH forms.
If you think in terms of a potential, the fermions trapped into it always have their wavefunction decaying exponentially beyond the surface of the potential, they remain trapped because there is no "valley" into which to tunnel (the gravitational potential is always below the vacuum). So as you add energy into the system, allowing ever higher harmonic levels inside the potential, general conservation of energy tells us that we build a depth of the gravitational potential increasing faster than higher harmonics are being occupied. I do not remember explicitly doing such a calculation, but if the depth would not grow fast enough, then our calculations would indicate that no black hole form, which is contrary to the general theorems and would only invalidate our approximations (the BH collapse is generic and does not require specific initial conditions such as spherical symmetry).
humanino said:I agree with tom.stoer and think his point is quite relevant to go beyond what has been said. So to clarify my post above in 2 points, I only meant 1) specifically where the concept of pressure degeneracy is used (to compute stability condition when collapse does to a BH does not occur) 2) the limitation within the potential approach, if we contradicted the general GR theorems for BH formation, we would only invalidate this approach, not the theorems (potential approach is non-relativistic btw)
billbray said:I was under the impression that the degenracy state was achieved in neutron stars of a certain mass, just microseconds before they collapse into a black hole. is that wrong??
The Pauli exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. In other words, no two fermions can have the same set of quantum numbers.
In the context of black holes, the Pauli exclusion principle applies to the particles that make up matter. As a black hole's gravitational pull becomes stronger, particles are forced closer together, and their quantum states become more restricted. This leads to an increase in the number of particles with the same quantum numbers, violating the Pauli exclusion principle.
No, black holes do not follow the Pauli exclusion principle. As matter collapses to form a black hole, the intense gravitational forces overcome the effects of the exclusion principle, resulting in a state where particles with the same quantum numbers can exist in the same location.
The relationship between black holes and the exclusion principle is that, as a black hole's gravitational pull becomes stronger, particles are forced closer together, and their quantum states become more restricted. This leads to an increase in the number of particles with the same quantum numbers, violating the Pauli exclusion principle. This phenomenon is known as "quantum pressure" and plays a crucial role in the understanding of black holes.
The violation of the Pauli exclusion principle in black holes has significant consequences. It leads to a state of matter with incredibly high densities and pressures, resulting in the formation of a singularity at the center of a black hole. This singularity is a point of infinite density, where the laws of physics, including the exclusion principle, break down.