# How does gravity acts on the electrons to collapse a neutrons star or white dwarfs against the degeneracy pressure?

if electrons is considered as quantum particle in case neutron star (alluding to quantum statistics) how does gravity makes the star collapse? considering the fact that electrons are quantum particles and have negligible mass.

• What you're asking for is effectively a theory of quantum gravity, which we don't have yet. – probably_someone Mar 29 '18 at 16:59
• then how do black holes form if we don't completely understands how gravity acts here – Kritika Mar 29 '18 at 17:02
• We know enough about general relativity to know that they have to exist. We can also deduce some of their basic properties from thermodynamics, and we can guess at some of their other basic properties by extending quantum field theory in a possibly-invalid way. But aside from that, we just don't know much about them. – probably_someone Mar 29 '18 at 17:30
• @probably_someone: Nonsense. This has been understood since the 1930's. It's one of the main things Chandrasekhar is known for. No quantum gravity is required. – user4552 Mar 29 '18 at 19:41
• @BenCrowell You're right, of course, in the case of neutron stars and white dwarfs. The question originally also mentioned black holes, which is why I said the things I did. – probably_someone Mar 29 '18 at 19:43

Chandrasekhar showed in the 1930's that there was a limit, now called the Chandrasekhar limit, on the mass of a white dwarf that is in hydrodynamic equilibrium. The limit is about 1.4 solar masses. This is enough to establish that a heavier star can't be a white dwarf, but by itself it doesn't explain what happens instead.

The reaction $\text{p}+\text{e}^-\rightarrow \text{n}+\nu$ occurs due to the weak nuclear force. When the proton is free, i.e., in hydrogen, it requires an input of 0.8 MeV of energy. A nucleus can absorb an electron and convert a proton into a neutron, and in this context the process is called electron capture. Ordinarily this process will only occur if the nucleus is neutron-deficient; once it reaches a neutron- to-proton ratio that optimizes its binding energy, neutron capture cannot proceed without a source of energy to make the reaction go. In the environment of a white dwarf, however, there is such a source. The annihilation of an electron opens up a hole in the “Fermi sea.” There is now an state into which another electron is allowed to drop without violating the exclusion principle, and the effect cascades upward. In a star with a mass above the Chandrasekhar limit, this process runs to completion, with every proton being converted into a neutron. This results in a neutron star.

A calculation similar to Chandrasekhar's, by Tolman, Oppenheimer, and Volkoff in 1939, shows that there is an upper limit on the mass of a stable neutron star. The limit is currently believed to be about 2 to 3 solar masses. Most likely there is no stable form of matter for stars above this limit, so they become black holes.

• I assume that the original calculation was based on Pauli's recent explanation of the exclusion principle for electrons? But, not knowing the energy of the reaction itself, how did he come up with 1.4? – Maury Markowitz Mar 29 '18 at 20:03
• @MauryMarkowitz: Instability doesn't depend on the existence of the weak-force reaction. The weak-force reaction explains why the instability doesn't result in runaway collapse to a black hole. – user4552 Mar 30 '18 at 0:51
• could u plz elaborate on the point of source of energy that keeps up the reaction? – Kritika Mar 30 '18 at 1:21
• also, what i am not able to understand is how the neutron star can turn to a black hole? – Kritika Mar 30 '18 at 1:23
• @BenCrowell - my comment is that there is nothing about why there is a limit. We know what's pulling it in, gravity, but what's stopping it? That Chandrasekhar had a calculation doesn't explain what it is, nor Tolman et al. That seems more germane to the original Q than the process of conversion. – Maury Markowitz Mar 30 '18 at 15:02

The acceleration on a particle due to gravity doesn't depend on its mass; it's just the local gravitational field strength. This is the basis of the equivalence principle.

at the field strengths present in a star near collapse, the mass of the electrons is not negligible. they are gravitationally bound.

Gravitation is not needed. Extremely high pressure is the only thing that is needed. Gravitation is one mechanism that can create the necessary pressure.

• how does gravitation creates pressure – Kritika Mar 30 '18 at 1:08
• Not to sound like I'm making a joke, but have you ever swum underwater? That pressure on your ears is due to gravity. That water is made up of (among other things) electrons. The process is the same in a star. If you really don't know how gravity produces pressure, you need to rewind your question to something much simpler. – Maury Markowitz Mar 30 '18 at 15:08

Gravity acts on electrons the same way it acts on any other mass. It doesn’t matter how small the electrons mass is. What causes gravity is another question.