[Kryptid]

Sorry, I disagree.

Too bad, because that's not what that means.

I clearly claim that Theory D doesn't violate any law of physics

Then that claim is wrong, because the idea of black holes being able to produce an unlimited amount of new mass-energy violates conservation of mass-energy.

Therefore, in the process of creating new particle we get extra kinetic energy.

This is the part where you violate conservation of energy.

[Dave Lev (OP)]

Dear Malamute
Please let me know if I understand you correctly.
1. virtual particles:

The mechanism of Hawking-Bekenstein (1) radiation implicitly assumes that the two virtual particles have opposite mass-energy signs, totaling zero...
In this view, virtual particles have both positive and negative mass-energy and how much of what shows up where depends on circumstances. So in general virtual particles do not fall on the mass shell except perhaps at the zero point.

So, the two virtual particles have opposite mass-energy signs. Therefore, as they orbit at the speed of light their total positive and negative mass-energy is zero. Therefore, their creation do not contradicts the conservation of law.
2. Ordinary Particles:
The Virtual particles should be transformed to ordinary partials.

The idea of Hawking-Bekenstein radiation is that virtual particle pairs created near the event horizon might be pulled apart by the strong gravity.

So again, the total positive energy in theordinery positive particle is identical to the total negative energy in the ordinery negative particle. Hence, we get two new real particles orbiting at the speed of light near the event of horizon, one with a positive energy and one with negative energy without consuming energy from the system itself and without contradicting the conservation of law of Mass/energy.
3. Absorbed into the black hole

The negative mass-energy particle would be absorbed into the black hole which would then contain less mass-energy. The positive energy would be free to escape, with its now real mass-energy being balanced by the loss of mass-energy of the black hole. No violation of mass-energy conservation.

As the real negative mass-energy particle would be absorbed into the black hole which would then contain less mass-energy, the other real positive mass-energy particle would be escape. Therefore during this process the decreasing amount of mass-energy in the BH is identical to the amount of the Mass-energy in the other free particle.
Please confirm.

[Kryptid]

Therefore during this process the decreasing amount of mass-energy in the BH is identical to the amount of the Mass-energy in the other free particle.

Congratulations. That is exactly how it works.

[Malamute Lover]

Dear Malamute
Please let me know if I understand you correctly.
1. virtual particles:

The mechanism of Hawking-Bekenstein (1) radiation implicitly assumes that the two virtual particles have opposite mass-energy signs, totaling zero...
In this view, virtual particles have both positive and negative mass-energy and how much of what shows up where depends on circumstances. So in general virtual particles do not fall on the mass shell except perhaps at the zero point.

So, the two virtual particles have opposite mass-energy signs. Therefore, as they orbit at the speed of light their total positive and negative mass-energy is zero. Therefore, their creation do not contradicts the conservation of law.
2. Ordinary Particles:
The Virtual particles should be transformed to ordinary partials.

The idea of Hawking-Bekenstein radiation is that virtual particle pairs created near the event horizon might be pulled apart by the strong gravity.

So again, the total positive energy in theordinery positive particle is identical to the total negative energy in the ordinery negative particle. Hence, we get two new real particles orbiting at the speed of light near the event of horizon, one with a positive energy and one with negative energy without consuming energy from the system itself and without contradicting the conservation of law of Mass/energy.
3. Absorbed into the black hole

The negative mass-energy particle would be absorbed into the black hole which would then contain less mass-energy. The positive energy would be free to escape, with its now real mass-energy being balanced by the loss of mass-energy of the black hole. No violation of mass-energy conservation.

As the real negative mass-energy particle would be absorbed into the black hole which would then contain less mass-energy, the other real positive mass-energy particle would be escape. Therefore during this process the decreasing amount of mass-energy in the BH is identical to the amount of the Mass-energy in the other free particle.
Please confirm.

Mostly. You are correctly understanding the mechanism of Hawking-Bekenstein radiation except that the two virtual particles do not become real until one of the virtual particles is pulled through the event horizon, which is where the necessary positive/negative energy to make them real comes from.

Some qualifying comments below:

The two virtual particles do not orbit each other. For the time that they exist, their motion is determined by interaction with whatever local forces are in effect, with the exception that they do not predictably obey the energy-momentum laws of motion, having positive and negative mass-energy components not necessarily in the same place in space.

Virtual particles do not travel at light speed unless they are photons, which have no rest mass.

Virtual particle pairs are opposite in more than positive/negative mass-energy. They are opposite in all quantum values – charge, spin etc. They are opposite in the same ways as normal matter and antimatter except that real (non-virtual) antimatter, the kind they make in particle colliders, has positive mass-energy. The two virtual particles can appear from nothing, sneaking under the Uncertainty Principle radar, and disappear into nothing because they add up to nothing. All values, including mass-energy exactly cancel out.


There are other concerns I have with the Hawking-Bekenstein mechanism but I need to hash them out in my head first before I can put them into words.

[Kryptid]

Nothing is ever pulled out.

I don't think that's what he's arguing. When he says "pulled through the event horizon", I think he means being pulled into the black hole from the outside.

[Malamute Lover]

You are correctly understanding the mechanism of Hawking-Bekenstein radiation except that the two virtual particles do not become real until one of the virtual particles is pulled through the event horizon

Reference please.  Nothing, not even virtual particles, can be pulled backwards in time.  The virtual particles form outside, which happens frequently, and occasionally one of the two manages not to be pulled in.  Nothing is ever pulled out.

I'd have to look up to get a decent wording of how the virtual particles are eventually imparted with positive and negative energy. I'm no expert.

 which is where the necessary positive/negative energy to make them real comes from.

I was explaining the mechanism of Hawking-Bekenstein radiation not giving my own opinion. As I alluded to earlier, I have problems with it myself.

Here is a math free overview.
https://en.wikipedia.org/wiki/Hawking_radiation#Overview

If you want an in-depth presentation of the mechanism of black hole radiation, try this.
https://www.brainmaster.com/software/pubs/physics/Hawking%20Particle%20Creation.pdf

Personally, I have been through Hawking’s 1975 paper a few times and I still get lost. (And this is less formal than his 1974 paper in Physics Review.)

The problem I have with the idea is that for one of the virtual particles to fall through the black hole takes only finite time from the viewpoint of that particle but infinite time from the viewpoint of the other particle which does not fall through. Since the energy of the escaping particle is supposed to be supplied by the captured particle being absorbed, that energy should only reach the escaping particle an infinite time in the future. I have tried to figure out whether this is accounted for in the math and it does not appear to be. The Hawking paper linked above discusses in a speculative manner about space-time maybe being quantized. This might reduce infinite time to finite time but the way I see it there must still be a delay and the mechanism does not work as advertised. One of the virtual particles is isolated from its partner for a non-zero time before getting the energy transfusion needed to become real. In quantum theory as I understand it, this is a non-starter situation.

[Dave Lev (OP)]

Congratulations. That is exactly how it works.

Thanks
However, I hope that we all agree by now that there is no way to bypass the conservation of mass/energy and it must be absolute.

Mostly. You are correctly understanding the mechanism of Hawking-Bekenstein radiation except that the two virtual particles do not become real until one of the virtual particles is pulled through the event horizon, which is where the necessary positive/negative energy to make them real comes from.

Some qualifying comments below:

The two virtual particles do not orbit each other. For the time that they exist, their motion is determined by interaction with whatever local forces are in effect, with the exception that they do not predictably obey the energy-momentum laws of motion, having positive and negative mass-energy components not necessarily in the same place in space.

Virtual particles do not travel at light speed unless they are photons, which have no rest mass.

Virtual particle pairs are opposite in more than positive/negative mass-energy. They are opposite in all quantum values – charge, spin etc. They are opposite in the same ways as normal matter and antimatter except that real (non-virtual) antimatter, the kind they make in particle colliders, has positive mass-energy. The two virtual particles can appear from nothing, sneaking under the Uncertainty Principle radar, and disappear into nothing because they add up to nothing. All values, including mass-energy exactly cancel out.

Thanks for your great explanation.
So, the total positive energy in the ordinary positive particle (matter) is identical to the total negative energy in the ordinary negative particle (antimatter).
They do not orbit each other and they do not orbit at the speed of light. So, at what speed they orbit at the moment of their creation near the event horizon?
The particle/matter has a positive energy and the antimatter/antiparticle has identical negative energy. therefore, they both do not consume energy for their creation from the system itself and without contradicting the law conservation of Mass/energy.
I assume that there is a possibility that if they stay long enough near each other, they should eliminate each other.
So, theoretically, some of the new created matter/antimatter or particles/antiparticles are eliminating each other before they even say "Good morning" to each other".
However:
1. Do you have an idea why the antimatter/antiparticles is falling into the BH while the other partial/matter is pulled through the event horizon? Why can't we assume the opposite? Could it be that our body is made out of antimatter?
2. As for any particle/matter there must be antiparticle/antimatter, than in order to fulfill the conservation law of mass/energy - the total mass of the antimatter in our whole Universe must be identical to the total mass of the matter.
However, if I understand it correctly, based on the BBT, the total mass of the matter is much bigger than the total mass of the antimatter.
So, how our scientists could claim that the conservation of mass/energy is absolute, while based on the BBT there is much more matter than antimatter in our universe? How could it be that during the Big Bang process, more matter had been created than antimatter?

[Kryptid]

However, I hope that we all agree by now that there is no way to bypass the conservation of mass/energy and it must be absolute.

And yet you'll soon be stating again that gravity can create energy, which violates conservation of energy...

1. Do you have an idea why the antimatter/antiparticles is falling into the BH while the other partial/matter is pulled through the event horizon? Why can't we assume the opposite?

In black holes that are small enough (and therefore hot enough) to produce matter and antimatter particles, it's random. The amount of matter and antimatter emitted by the black hole is roughly equal because both respond to gravity in the same way.

So, how our scientists could claim that the conservation of mass/energy is absolute, while based on the BBT there is much more matter than antimatter in our universe?

Your model has the same problem, since black holes should release antimatter at the same rate as matter.

[Malamute Lover]

So, the total positive energy in the ordinary positive particle (matter) is identical to the total negative energy in the ordinary negative particle (antimatter).

In real (non-virtual) particles, both matter and antimatter have positive mass-energy.

Virtual particle pairs pop up spontaneously all over the place because the Uncertainty Principle says they can. These pairs have opposite signs in all quantum values, including mass-energy. They disappear spontaneously, annihilating each other completely because they exactly cancel out to zero.

They do not orbit each other and they do not orbit at the speed of light. So, at what speed they orbit at the moment of their creation near the event horizon?

They are not in any kind of orbit. The lowest possible orbit is well above the event horizon. An orbit is a path that can followed around a gravitating body without exerting any additional force. From near the event horizon it is possible to go up (hard) or down (easy) but it is not possible to stay at the same level without applying continuous force. The gravitational gradient – the difference in gravitational force between two levels – is much too high.

What motion the virtual particles may have at creation is not predictable. Recall that they do not strictly obey energy-momentum rules and real particles do. This is called being off the mass shell.

The particle/matter has a positive energy and the antimatter/antiparticle has identical negative energy. therefore, they both do not consume energy for their creation from the system itself and without contradicting the law conservation of Mass/energy.
I assume that there is a possibility that if they stay long enough near each other, they should eliminate each other.
So, theoretically, some of the new created matter/antimatter or particles/antiparticles are eliminating each other before they even say "Good morning" to each other".

The lifetime of a virtual particle pair is limited by the amount of rest mass in the equivalent real (on the mass shell) particles. The mathematics of the Heisenberg Uncertainty Principle regulates how long a given mass can exist ‘under the radar’. The more the mass of the real particle equivalent, the shorter the time allowed.e

One way to think of a virtual particle pair is that it is really a single particle making a little loop in time, positive mass-energy in one direction and negative mass-energy in the other. The time reversal would also account for the reversal of the quantum numbers as well.

Since photons have zero rest-mass, virtual photons can exist forever. Virtual photons are the carriers of the electromagnetic force, with photon and anti-photon virtual particles exchanged between the two charged bodies, like electrons.

However:
1. Do you have an idea why the antimatter/antiparticles is falling into the BH while the other partial/matter is pulled through the event horizon? Why can't we assume the opposite? Could it be that our body is made out of antimatter?

Good observation. That is a question I have also. It seems to me that which one should be absorbed should be random, with a net balance of no change and no Hawking-Bekenstein radiation. OTOH if one considers the negative mass-energy particle to be going backward in time, it should be the one escaping and the positive mass-energy one going into the event horizon.  But to understand what really happens in a strong gravitational field in detail requires calculation. And at my age I have absolutely no intention of ever looking at tensors again, much less horribly non-linear ones.

Whether we are labeled matter or antimatter is a ‘matter’ of convention. All the real mass-energy in the universe having the same sign is what, ahem, ‘matters’.

2. As for any particle/matter there must be antiparticle/antimatter, then in order to fulfill the conservation law of mass/energy - the total mass of the antimatter in our whole Universe must be identical to the total mass of the matter.
However, if I understand it correctly, based on the BBT, the total mass of the matter is much bigger than the total mass of the antimatter.
So, how our scientists could claim that the conservation of mass/energy is absolute, while based on the BBT there is much more matter than antimatter in our universe? How could it be that during the Big Bang process, more matter had been created than antimatter?

First, the absence of anti-matter at large in the universe violates symmetry laws but not mass-energy conservation.  Real anti-matter has positive mass-energy just like real normal matter.
 
In high energy collider events, matter and anti-matter are both produced in equal proportions. There is no ‘law’ against antimatter. It is a very good question why the universe at large has only matter. There should have been equal amounts of each type. Since matter and anti-matter cancel each other’s quantum values, they should have all become energy in the form of photons. Matter with mass should not exist. Yet obviously it does.

One possibility is an oddity in quantum theory. A particle called the B meson has the most unusual property of oscillating between matter and anti-matter states. That is, it spontaneously reverses all its quantum signs. Not mass-energy of course. That always remains positive. This is a real particle, not a virtual particle pair. The Standard Model predicts not only this but that it should spend a touch more time in the matter state than the antimatter state. This has been confirmed experimentally at both Fermilab and at CERN although they disagree somewhat on the exact numerical values involved.

In the B meson scenario, as the original (hypothesized) equal amounts of matter and antimatter annihilated each other into photons, these energetic photons decayed into more matter and antimatter particles. But among the new particles would be B mesons, which would stack the deck in favor of normal matter. Eventually everything would pass through a B meson state and things would settle down to only normal matter and photons.  The B meson is a very massive particle and decays quickly into other particles. It has enough mass to decay into the familiar (and stable) protons, neutrons, electrons etc. that we are familiar with.

I have an idea of my own that the bias toward familiar matter could be related to a mechanism I proposed that caused all mass-energy in the universe to have a positive sign. For the mass-energy part of the idea see:
https://www.thenakedscientists.com/forum/index.php?topic=79979.0

I have not gotten around to extending this idea into the matter/antimatter issue because it is complicated, involving Charge Parity Time symmetry violations. I need to dig into recent experimental results at CERN before finalizing the idea.

[Dave Lev (OP)]

First, the absence of anti-matter at large in the universe violates symmetry laws but not mass-energy conservation.  Real anti-matter has positive mass-energy just like real normal matter.

Thanks Malamute
So, you claim that the absence of anti-matter at large in the universe violates symmetry laws.
Let's try to find a solution for that:
We already know that due to the mechanism of Hawking-Bekenstein the decreasing amount of mass-energy in the BH is identical to the amount of the Mass-energy in the other free particle.
In other words, as one of the pair (antiparticle/antimatter) is falling in, the other one (particle/matter) is ejected outwards.
Our scientists assume that the SMBH is only made out of matter. Therefore, the falling matter should decrease the mass of the SMBH.
However, we really don't know if it is made out of matter or antimatter as in both cases they have a positive mass energy and the same gravity force.
Hence, if the falling particle is antimatter, why can't we just assume that the SMBH is made out of antimatter?
In this case, we might find that the total matter in the whole Universe is identical to the total Antimatter that is existed inside all the BH+MBH+SMBH in our universe.
Therefore, we can get a perfect balance between the antimatter to the matter.
Hence, do you agree that in this case we can't claim that there is absence of anti-matter in our universe and therefore, our universe doesn't violate the symmetry law any more?

[Bored chemist]

, why can't we just assume that the SMBH is made out of antimatter?

Because, if there was that much antimatter about, it would have been annihilated by reaction with normal matter before it got the chance to form a black hole.

However, Kryptid's point makes it irrelevant,.

[Kryptid]

Hence, if the falling particle is antimatter, why can't we just assume that the SMBH is made out of antimatter?

A black hole made from the collapse of antimatter is identical to one made from the collapse of matter. This is one of the things that is meant by the phrase "black holes have no hair".

[Dave Lev (OP)]

, why can't we just assume that the SMBH is made out of antimatter?

Because, if there was that much antimatter about, it would have been annihilated by reaction with normal matter before it got the chance to form a black hole.

You have missed the point.
How antimatter by itself could annihilate itself?
We claim that the SMBH is ONLY made out of antimatter.
The falling matter is also ONLY antimatter.
So, as falling antimatter gets to a big barrel of antimatter, how can you claim for annihilated by reaction with normal matter while there is no normal matter?

A black hole made from the collapse of antimatter is identical to one made from the collapse of matter. This is one of the things that is meant by the phrase "black holes have no hair".

So, do you agree that a SMBH could be made only by antimatter?

[Kryptid]

So, do you agree that a SMBH could be made only by antimatter?

It could happen in principle, but it's extremely unlikely since there is so little antimatter in the Universe.

[Dave Lev (OP)]

So, do you agree that a SMBH could be made only by antimatter?

It could happen in principle, but it's extremely unlikely since there is so little antimatter in the Universe.

Thanks
So, you agree that in principle the SMBH could be full with antimatter.
However, you claim that it is extremely unlike.

Now, do you accept the idea of symmetry law?
If so, and as you claim: "there is so little antimatter in the Universe", than in order to balance the symmetry law, the antimatter must be accumulated somewhere.
Hence, don't you agree that in order to fulfill the symmetry law, the antimatter should be accumulated at those big barrels that we call BH or SMBH? Therefore, the chance that the BH/SMBH is full with Antimatter is almost 100% or at least very high?

[Bored chemist]

So, do you agree that a SMBH could be made only by antimatter?

It could happen in principle, but it's extremely unlikely since there is so little antimatter in the Universe.

Thanks
So, you agree that in principle the SMBH could be full with antimatter.
However, you claim that it is extremely unlike.

Now, do you accept the idea of symmetry law?
If so, and as you claim: "there is so little antimatter in the Universe", than in order to balance the symmetry law, the antimatter must be accumulated somewhere.
Hence, don't you agree that in order to fulfill the symmetry law, the antimatter should be accumulated at those big barrels that we call BH or SMBH? Therefore, the chance that the BH/SMBH is full with Antimatter is almost 100% or at least very high?

No
At best it is 50:50
Either  it's in the SMBH, or the symmetry is broken.
We have no way to say which.

However, there is at least one reason to say that it's not in the SMBH- it would have reacted with normal matter before it got a chance to form black holes.

So it's not "almost 100%", it's practically zero.

[Malamute Lover]

First, the absence of anti-matter at large in the universe violates symmetry laws but not mass-energy conservation.  Real anti-matter has positive mass-energy just like real normal matter.

Thanks Malamute
So, you claim that the absence of anti-matter at large in the universe violates symmetry laws.
Let's try to find a solution for that:
We already know that due to the mechanism of Hawking-Bekenstein the decreasing amount of mass-energy in the BH is identical to the amount of the Mass-energy in the other free particle.
In other words, as one of the pair (antiparticle/antimatter) is falling in, the other one (particle/matter) is ejected outwards.
Our scientists assume that the SMBH is only made out of matter. Therefore, the falling matter should decrease the mass of the SMBH.
However, we really don't know if it is made out of matter or antimatter as in both cases they have a positive mass energy and the same gravity force.
Hence, if the falling particle is antimatter, why can't we just assume that the SMBH is made out of antimatter?
In this case, we might find that the total matter in the whole Universe is identical to the total Antimatter that is existed inside all the BH+MBH+SMBH in our universe.
Therefore, we can get a perfect balance between the antimatter to the matter.
Hence, do you agree that in this case we can't claim that there is absence of anti-matter in our universe and therefore, our universe doesn't violate the symmetry law any more?

You seem to be confusing negative mass-energy particles with antimatter. The antimatter produced in collider events has positive mass-energy. It just has other quantum values reversed – negative charge protons, positive charge electrons etc.

By contrast, virtual particle pairs have one with positive mass-energy and the other with negative mass-energy. The is no reason that the positive mass-energy one has to be normal matter, e.g., positive charge protons. It could be antimatter, e.g., negative charge protons.  The same for the negative mass-energy partner. The negative mass-energy partner would have opposite quantum values to keep conservation laws. Unless there is some unknown mechanism at work, a half and half distribution would be expected.

Black holes have the usual ‘down’ kind of gravity, attracting matter in spirals that we see getting denser and hotter as they get closer to the black hole. Black holes cannot consist of negative mass-energy because that would be repulsive instead of attractive.

Since there is as far as we know no noticeable amount of antimatter (positive mass-energy remember) in the universe at large, the accumulation of enough anti-matter in one neighborhood to make a SMBH, or even a small one, is extremely improbable.

For the matter/antimatter symmetry to be resolved by black holes being antimatter would require that the mass of all matter in the universe not in black holes be equal to the amount of mass in black holes. While there are SMBH in the heart of most galaxies, they constitute only a tiny fraction of the mass of the galaxy. (Not counting dark matter) Other black holes within a galaxy contribute only a miniscule amount to the black hole mass total.  Unless there are somehow a whole bunch of black holes or truly colossal ones that have not been noticed, this condition is not satisfied.

There are undoubtedly weird things to be discovered about the universe, but this does not seem to be one of them. But keep trying! Who knows?

[Kryptid]

Hence, don't you agree that in order to fulfill the symmetry law, the antimatter should be accumulated at those big barrels that we call BH or SMBH? Therefore, the chance that the BH/SMBH is full with Antimatter is almost 100% or at least very high?

Absolutely not. There is no evidence for it. Black holes do not preferably ingest antimatter over matter. It is equally likely to consume either one.

[Dave Lev (OP)]

You seem to be confusing negative mass-energy particles with antimatter.

No, I'm not confused

Black holes have the usual ‘down’ kind of gravity, attracting matter in spirals that we see getting denser and hotter as they get closer to the black hole. Black holes cannot consist of negative mass-energy because that would be repulsive instead of attractive.

Yes, I fully agree.
Therefore, we only discuss on new created particle pair (Particle/matter + antiparticle/antimatter) with positive mass energy.

The antimatter produced in collider events has positive mass-energy. It just has other quantum values reversed – negative charge protons, positive charge electrons etc.

Yes again. We discuss on antimatter with positive mass energy.
So, for example the new created particle pair could be as follow:
Particle/matter - Positive charge as electrons
Antiparticle/Antimatter - Negative charge as protons.

Black holes do not preferably ingest antimatter over matter. It is equally likely to consume either one.

Well, you discuss about the matter that it consumes.
However, I discuss about the matter inside the BH.
Do you agree that the chance to have a BH with antimatter might be similar to the chance for a BH with matter?
So, let's go back to Hawking-Bekenstein mechanisn
We already know that due to that mechanism as one of the pair (antiparticle/antimatter) is falling in, the other one (particle/matter) is ejected outwards.
Therefore, for a BH which is based on matter, falling antimatter should decrease its mass and eventually it must be evaporated.
However, in the same token, for a BH which is based on Antimatter, a falling Antimatter should increase its mass.
Hence, Hawking had estimated that in the case of a black hole (with matter) formed in the early universe with a mass of less than approximately 10^15 g would have evaporated completely by the present day.
However, it is very clear that for a BH with antimatter should increase its total mass due to the falling antimatter.
Therefore, statistically we could have two kinds of BHs
One kind of BH must be evaporated over time while the other kind must increase its mass over time.

Therefore, this could also be the answer for the following problem of the symmetry law:

For the matter/antimatter symmetry to be resolved by black holes being antimatter would require that the mass of all matter in the universe not in black holes be equal to the amount of mass in black holes. While there are SMBH in the heart of most galaxies, they constitute only a tiny fraction of the mass of the galaxy. (Not counting dark matter) Other black holes within a galaxy contribute only a miniscule amount to the black hole mass total.  Unless there are somehow a whole bunch of black holes or truly colossal ones that have not been noticed, this condition is not satisfied.

The total created amount of matter from day one of the Universe is identical to the total created antimatter.
However, as many BHs had been evaporated, we think that there is no balance.
Therefore, In the core of the Milky Way Galaxy there is a SMBH which is full with antimatter.
Due to the new created particle pair process around it, one antiparticle is falling in and increases it mass, while the other one is ejected outwards and also increasing the total matter around it.
Therefore, do you agree that we can get a system that simultaneously increases the total Antimatter mass of the SMBH and the matter around the BH without violating the symmetry law or the conservation of energy law?

[Kryptid]

However, I discuss about the matter inside the BH.

I've already told you, black holes themselves are neither matter nor antimatter.

Do you agree that the chance to have a BH with antimatter might be similar to the chance for a BH with matter?

Yes, the case is zero for both. See my previous reply.

We already know that due to that mechanism as one of the pair (antiparticle/antimatter) is falling in, the other one (particle/matter) is ejected outwards.

That's wrong. Either the matter or the antimatter particle can fall in or escape. The probability is equal for both because both respond identically to gravity.

Therefore, for a BH which is based on matter, falling antimatter should decrease its mass and eventually it must be evaporated.
However, in the same token, for a BH which is based on Antimatter, a falling Antimatter should increase its mass.

Black holes aren't made of matter or antimatter, like I said before. They are basically raw mass/energy with a couple of other properties such as spin and electric charge. It's meaningless to call it either matter or antimatter. What causes the black hole to evaporate is the consumption of negative mass/energy, not antimatter.

Due to the new created particle pair process around it, one antiparticle is falling in and increases it mass, while the other one is ejected outwards and also increasing the total matter around it.

No, that breaks conservation of mass.

Therefore, do you agree that we can get a system that simultaneously increases the total Antimatter mass of the SMBH and the matter around the BH without violating the symmetry law or the conservation of energy law?

No.