The baryon and lepton number of a black hole

The baryon number and lepton number

The baryon number is the number of baryons minus the number of antibaryons. Here on Earth this usually turns out to be the number of protons minus the number of antiprotons plus the number of neutrons minus the number of antineutrons.         (1.1)

The lepton number is the number of electrons minus the number of positrons plus the number of neutrinos minus the number of antineutrinos.         (1.2)

By example a Helium-4 atom: 2 protons and 2 neutrons in the nucleus and 2 electrons circling around it. The baryon number of the He-4 atom is 4, the lepton number is 2.

For convenience we shall take that baryon numbers as well as lepton number always add (never subtract), and that
particles have positive baryon number or positive lepton number
while
antiparticles have negative baryon number or negative lepton number.

This is meant as precisely the same rule as (1.1) and (1.2), only defined in a little different way.         (1.3)
 

The black hole

Black holes can be formed from any matter that has mass, but in astronomy two kinds are dominantly present: black holes formed by the collapsing remnants of large stars and black holes formed because a million stars in the center of a galaxy are too near to each other.         (2.1)

Take a sufficiently large star collapsing to a black hole. First the star passes the stage of a neutron star: all electrons are pushed into the protons and in doing so turning them into neutrons. For every electron that is absorbed by a proton an electron neutrino is given back to the universe in stead of the electron, in order to conserve lepton number. Well, that is, this sentence is in fact stated wrong, it should be: every electron is converted into an electron neutrino and a W- particle and the W- particle then converts one proton in a neutron. The electron neutrinos escape the star. The baryon number of the neutron star is equal to the total number of neutrons in it, the lepton number of the star is zero (provided the neutron star is not electrically charged). This is what is going to to collapse to a black hole, providing mass is sufficiently large.         (2.2)

Is it possible to assign a specific baryon or lepton number to a black hole? When a mass becomes a black hole, the matter of that mass, the elementary particles it consists of, are no longer accessible by any means. In accordance with the spirit of QED and QM this means that at the moment the black hole is formed, to the original content is added the superposition of all other possible contents that could have yielded this black hole. Amongst these is the one that allready consists of just the right number of photons for Hawking evaporation. We don't deal with only the original neutrons of the neutron star, instead we have to deal with a lot more possibilities. Those superposed contents might have very different baryon and lepton number.         (2.3)

So I would conclude:

Assigning a specific baryon or lepton number to a black hole is not possible         (2.4)

There is no way to distinguish one content out of all possible contents in a black hole, until a measurement has been made, and that's impossible with a black hole.

It is often said a black hole has no hair. A black hole has only three properties that are left behind on the event horizon where time is standing still (as observed by us on Earth): mass, electric charge and impulse momentum. Once in a black hole, as is usually said, irregular mass distributions, electric currents, magnetic fields, matter-or-antimatter and baryon number and lepton number, all become unobservable at the moment the black hole forms.

Black hole forming might violate baryon and lepton number conservation laws.         (2.5)

E.g. the forming of a black hole from a neutron star violates baryon number conservation law by the amount of the number of neutrons in the star. And that's not because of an illegal disappearance of particles, but just because the part of spacetime where the neutron star is in has been clipped out of our observable universe.
 

Some thought experiments

The neutrons spoil the picture I want to sketch. Let's get rid of them by a thought experiment. A gamma ray is directed to every neutron on the surface of the neutron star and gives the neutron sufficient energy to split in a proton and an electron and an anti electron neutrino. The anti electron neutrinos escape the neutron star. The proton is free now, the energy of the gamma ray was sufficient to release it and give it a small velocity to stay free for a (not too) small amount of time. One electron combines with the proton to form a H-atom. Soon all of the neutron star is converted into a cloud of single hydrogen atoms. I assume this resembles the primordial cloud where the former neutron star did originate from. Let this cloud of one star mass be the matter that is going to collapse to a black hole. The baryon number of the cloud is the number of protons, the lepton number of the cloud is the number of electrons. The lepton number is equal to the baryon number now, provided the black hole has no net electric charge.         (3.1)

The H-cloud situation as far as the baryon and lepton numbers are concerned, resembles the best the situation in which a million stars in the center of a galaxy form a large black hole.         (3.2)

Any black hole will finally evaporate by Hawking radiation. The Hawking radiation consists of photons, most of the time photons of very long wave radiation. Photons have baryon number zero and lepton number zero.         (3.3)

So in the example described above, one star mass of an equal amount of baryons and leptons is converted by Hawking radiation in photons of lepton number zero and baryon number zero. This is a large violation of baryon number and lepton number. How black holes do that?         (3.4)

The original neutron star we started with has a baryon number equal to the number of neutrons in the star and a lepton number zero. Still bad, but better already than (3.4).         (3.5)

Is there a change there can be fumbled at the baryon number and lepton number of the photon? As long as the black hole mass is still high, it radiates only very low energy photons. These photons can be observed from a frame of reference moving with very high speed opposite to that of the photons, so that by Doppler effect the photon from the black hole has enough energy for the reaction

photon e- e+   (e- = electron, e+ = positron)

The lepton number of the right side of the equation is

1 - 1 = 0

The law of the conservation of lepton number says the lepton numbers of the right side and of the left side are equal, so the photon definitely has lepton number zero.

We can give our frame of reference from which we observe the Hawking radiation a still higher velocity, in order to give the Hawking radiation photons energy for the reaction

photon p+ p-   (p+ = proton, p- = antiproton)

The baryon number of the right side of the equation is

1 - 1 = 0

The law of the conservation of baryon number says the baryon numbers of the right side and of the left side are equal, so the photon definitely has baryon number zero too.

So no, there cannot be tampered with the baryon or lepton number of the photon, both will stay zero.         (3.6)

The forming of a black hole from a sufficiently dense H-cloud (large baryon number and lepton number of same size) and its subsequent evaporation into low energy photons (lepton and baryon number zero) violates baryon and lepton conservation laws to the amount of the baryons and leptons that were present in the clipped-out part of spacetime.         (3.7)
 

The baryon-lepton number

Following the rule from (1.3), particles have positive baryon number or positive lepton number, and antiparticles have negative baryon number or negative lepton number. In paragraph Electrons as Baryons at page 4 of QG is argued the positron is the particle and the electron is the antiparticle. In TONE electrons and positrons are proposed as quarks with color white or black, colorless colors that don't glue. Then electrons are a kind of baryons. It suggests you may

Add the baryon number and lepton number to one combined baryon-lepton number         (4.1)

It opens the possibility that the black-hole-to-be H-cloud from (3.1) consists of a positive baryon number (the p+) and a negative lepton number of same size (the e-), adding up to a baryon-lepton number zero, in accordance with the photon cloud into which the black hole will evaporate.         (4.2)

According to page 4 of QG, the colors of the electron e-, positron e+, electron neutrino e, anti electron neutrino e, photon ph, weak force particle W and the neutrinophoton ph, are given as follows:

        (4.3)

In scheme (4.3) the e- and the e both have color -1 and thus both are antiparticles and have negative lepton number. So the system of our neutron star (large positive baryon number) plus the expanding cloud of e (large negative lepton number of equal size) together still has baryon-lepton number zero. But the cloud of e had escaped and when the neutron star collapses into a black hole the e are not included. Then there is an intermediate state of clipped-out spacetime called black hole with undefined baryon or lepton number. And then the black hole is replaced by a photon cloud of lepton number and baryon number zero. Far out there still are the e that embody a large negative lepton number. What is left is a large violation of baryon number due to the final disappearce of the neutrons in the neutron star.         (4.4)

Lepton number conservation law is obeyed (all e- replaced by e) but baryon number conservation law is not. To obey baryon-lepton number conservation law, one can invoke the emission of e along with the photons in the Hawking radiation. The disappeared neutrons are replaced by the same number of e. (Both e and neutrons are particles and not antiparticles, see the (4.3) scheme.)         (4.5)

So:

1) IF the event horizon of the black hole has no remembrance to the original content of neutrons THEN QED summons all other possible contents next to the original neutrons in the black hole and baryon number is not conserved.         (4.6)

Or:

2) The event horizon of the black hole HAS a remembrance to the original content of neutrons. Then there is no superposition of all possible contents, and:

a) When evaporating the Hawking radiation contains the needed number of e along with the low energy photons. The baryon conservation law is still violated, but the baryon-lepton number as being zero, is conserved: the e and the cloud of e from the forming of the neutron star cancel each others lepton number. At the black hole's event horizon there is an extra difference visible (the e) between black holes of neutron star matter origin and black holes of a millions stars too-near-to-each-other origin.         (4.7)

b) I guess black hole evaporation by neutron emission is not possible, isn't it? I worked it out a little in A previous attempt below. Neutron emission could obey baryon and lepton conservation laws in the black hole forming-and-evaporation process, without the need for a baryon-lepton number conservation law.
 

Antimatter black holes

According to the picture sketched in page 2 of EXPAN, antimatter goes backward in time, and when the antigravitation of an antimatter neutron star reaches through the time border into our forward time evolving region, this antigravitation is observed by us as an expanding force, expanding space between objects. Now the antimatter star in its own frame collapses into a black hole. (In our frame its forming is at the end of the antimatter neutron star's life as we observe it, in our future.) Just as it in our part of the universe would be, during the collapse the gravitational field outside the original surface of the star doesn't change a). Only the new space between the original surface of the star and the event horizon of the black hole is filled with neatly connected new gravitational field. So the gravitational field of the antimatter black hole, when reaching our part of the universe, is still the same influence (virtually the same) as it was when the star was still an antineutron star.

So the property of a black hole being formed from matter or antimatter is visible to the outside.         (5.1)

According to paragraph Dark Mechanics at page 2 of QG, antimatter mass is counted as negative mass. Although dark mechanics is not yet settled, I propose to

Assign a positive mass to black holes of matter origin and assign a negative mass to black holes of antimatter origin.         (5.2)
 

How did the baryon and lepton number of the universe start out?

According to (5.3) in paragraph Remnant particles in the fermion explosions at page 4 of EXPAN, the matter part of the universe where we are in now is the result of an extra fermion explosion. The line below (5.3) refers to the paragraph The GODevil particle at page 6 of EXPAN. The GODevil particle is the origin of the extra fermion explosion. There is argued the baryon-lepton number of the GODevil particle is zero, and so is the baryon-lepton number of the part of the universe covered by our extra fermion explosion.         (6.1)
 

A previous attempt

2 b) That the black hole emits neutrons as Hawking radiation, I guess that has a far too low chance to occur because of the large neutron mass. How would that work anyway? A n-n pair (n is an antineutron) appearing at the event horizon, then always the n is directed to the outside while the n always is directed inside (*) and subsequently those n search for the original neutrons in the neutron star to annihilate with them to... gamma rays. The gamma rays struggle to get out and red shift to the low energy photons of the actual Hawking radiation. With every emitted neutron there are emitted two photons too.

At the event horizon time is standing still. When approaching the event horizon, matter has still lesser elapse of time. Matter that falls into the hole takes infinite time (as observed by us from Earth) to actually reach the event horizon. So within the finite time of the entire Hawking evaporation all of the matter is still outside the black hole's event horizon: the n-n pairs, the n remainings and the original neutrons from the neutron star and the gamma rays from their annihilation. It looks as if the scenario from the previous alinea might be possible.

Does the energy picture fit? We started with a neutron star (accompanied by a far-away cloud of e) and ended with separated neutrons. To achieve the state of separated neutrons the binding energy of the neutrons in the neutron star has to be delivered somehow. When the n fall in, they gain kinetic energy and when this kinetic energy matches the binding energy then n-n annihilation takes place. It looks as if the energy picture might fit.

The whole black hole being just a bad dream? Never mind, this is all nonsense, I guess. There is no way to achieve (*). And the n won't find the n of the original neutron star, isn't it, and so the annihilation can't take place. Anyway, the black hole would evaporate by photon emission alone long before it could have evaporated by neutron-photon emission.

So 2 b) is a previous atttempt.