Pauli exclusion in some stars leads to degeneracy and explanations of how and why stars have the sizes, temperatures, and compositions they appear to have.
Some red giants and other large stars are said to have electron degeneracy operating in some part of the star. It means the electrons are so close together that Pauli exclusion modifies the equation of state, Temperature, Pressure, and Volume.
White dwarfs are thought to be proton degenerate near the centers also leading to a different equation of state that may describe some part or maybe almost all of the star.
Neutron stars are believed to be neutron degenerate, with yet another equation of state.
Black holes can be regarded as degenerate time and space, which might simply disappear if some principle related to Pauli exclusion did not prevent it. The model is made of ZPE oscillators with virtual particle pairs packed so closely together that they can't vibrate independently.
Most of these explanations are nearly a hundred years old, and are probably not the best available now, but some of them can be found in old books written by famous pioneers in Astrophysics.
I have some arguments about black holes that can't be resolved here, and don't change the answers to your question.
Since time and space can become degenerate in a high gravity case, time and space should also become degenerate in a case of high acceleration, and maybe in cases of extremely high kinetic energy. It is discussed in other threads.
Pauli exclusion in some stars leads to degeneracy and explanations of how and why stars have the sizes, temperatures, and compositions they appear to have.
Some red giants and other large stars are said to have electron degeneracy operating in some part of the star. It means the electrons are so close together that Pauli exclusion modifies the equation of state, Temperature, Pressure, and Volume.
White dwarfs are thought to be proton degenerate near the centers also leading to a different equation of state that may describe some part or maybe almost all of the star.
Neutron stars are believed to be neutron degenerate, with yet another equation of state.
Black holes can be regarded as degenerate time and space, which might simply disappear if some principle related to Pauli exclusion did not prevent it. The model is made of ZPE oscillators with virtual particle pairs packed so closely together that they can't vibrate independently.
Most of these explanations are nearly a hundred years old, and are probably not the best available now, but some of them can be found in old books written by famous pioneers in Astrophysics.
I have some arguments about black holes that can't be resolved here, and don't change the answers to your question.
Since time and space can become degenerate in a high gravity case, time and space should also become degenerate in a case of high acceleration, and maybe in cases of extremely high kinetic energy. It is discussed in other threads.
None of these violates the PEP. Indeed WD and NSs are BECAUSE of PEP. Because a star most massive than 3 Solar mass cannot be supported by neutron degeneracy pressure, the gravity becomes dominant and rapid collapse starts. At a time the trapped surfaces form in which singularity is formed. Ultimately when the entire matter is trapped (from point of no return) the even horizon shows up. Inside the event horizon the role of time and space is reversed. Outside, time time flow is inevitable. Inside, movement along space coordinate is inevitable. Finally, the volume become almost zero, classically, but hopefully the entanglement of spacetime fabric confuses matter and it settles into a time non-settling (constantly changing) state.
In black holes evrything is vioalted, including common sense; they are totally unrealistic objects.
Bhs are not NOT UNREALISTIC objects as we study their properties, albeit indirectly, on a daily basis and hundreds are astronomers are satisfied with the measured compactness and mass. There are at least 20 stellar BHs whos masses mave been measured using properties close to 5-10 Schwarzschild radii. As to PEP violation, this is another story: You do not know it is obeys PEP or do not obey PEP. Their singular dense structure is such that the normal PEP or any other law for that matter, must be reformulated in strongest gravity limit. PEP suggests simultaneously two particles of same half-integral spin are not allowed. What is the meaning of simultaneity in this strongest gravity limit? So let's not talk about violating a law without knowing what the proper form of law is in that limit.
Your question is an important one, and it was addressed by Stephen Hawking in his book The Theory of Everything:
"When a star becomes small, the matter particles get very near each other. But the Pauli Exclusion principle says two matter particles cannot have both the same position and the same velocity. The matter particles must therefore have very different velocities. This makes them move away from each other, and so tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life the gravity was balanced by the heat.
(Subrahmanyan) Chandrasekhar realized, however, that there is a limit to the repulsion that the exclusion principle can provide. The theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light. This meant that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. Chandrasekhar calculated that a cold star of more than about one and a half times the mass of the sun would not be able to support itself against its own gravity. This mass is now known as the Chandrasekhar limit.
Chandrasekhar had shown that the exclusion principle could not halt the collapse of a star more massive than the Chandrasekhar limit."
Relativistic Fermi gas equation of state is P=k2 ρ4/3, in this case radius of the white dwarf decreases with (increasing) mass and it vanishes at a limit M0. This is known as Chandrasekhar limit. Nowhere in the derivation Pauli's exclusion principle breaks down. Rather the electron degeneracy pressure, which opposes gravitational effects, cannot compete against gravitational collapse.
The Pauli Exclusion Principle is at the heart of electron degeneracy pressure. Thus PEP violation is implicit in the gravitational overcoming of electron degeneracy pressure.
You don't need to break PEP. Calculate electron degeneracy pressure using the fact that PEP is correct. Then for large masses of the white dwarf star calculated value of (outward) electron degeneracy pressure will not be able to sufficiently oppose it's inward gravitational collapse.
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