Black holes and the scarcity of anti-matter

[baric]

I was reading the latest issue of Astronomy today. There was a nice article on antimatter and a short article about a simulation with two neutron stars that merged into a black hole. Very interesting stuff, as usual!

 

I started thinking about the ramifications of anti-matter and black holes and wondered if the matter-antimatter assymetry could be explained by it.

 

For example, if an anti-matter particle enters an event horizon, it will produce a corresponding amount of high-energy photons when it inevitably collides with normal matter. However, these photons are trapped within the EH and ultimately increase the mass of the black hole as they are pulled back to its center. In other words, the mass loss from the matter-antimatter annihilation becomes moot if it occurs within an EH.

 

This means that black holes would be effectively neutral with regards to matter-antimatter and could therefore explain the antimatter imbalance.

 

Of course, it would also logically mean that the majority of mass in the universe is contained within black holes!

 

 

I am not a physicist nor an astronomer. Someone please explain where my thinking is flawed on this subject.

[ajb]

For example, if an anti-matter particle enters an event horizon, it will produce a corresponding amount of high-energy photons when it inevitably collides with normal matter. However, these photons are trapped within the EH...

 

Right, so for the rest of us outside we will never know what happened to the antimatter particle.

 

...and ultimately increase the mass of the black hole as they are pulled back to its center. In other words, the mass loss from the matter-antimatter annihilation becomes moot if it occurs within an EH.

 

This sounds a bit naive. There is no mass loss if a particle and antiparticle collide behind the event horizon. In general relativity one takes mass and energy to be equivalent (well, it is all really much more complicated, but for a black hole this is fine). As an aside a black hole is only characterised by the mass, angular momentum and electric charge.

 

 

This means that black holes would be effectively neutral with regards to matter-antimatter and could therefore explain the antimatter imbalance.

 

What do you mean by this? One does expect physical black holes to be nearly electrically neutral in general.

 

Of course, it would also logically mean that the majority of mass in the universe is contained within black holes!

 

This is a prediction of your "theory". Indeed most of the mass of Universe does appear to be missing, see dark matter. Black holes and brown dwarfs make up what are known as MACHOs, that is Massive Compact Halo Objects. Current thinking is that MACHOs do not contribute significantly to dark matter. It is believed that non-baryonic dark matter is the dominant component of dark matter.

 

So, I think it is unlikely that your "theory" is consistent with observation, but one has to do the maths to show this. That is we would need to know the density of black holes you require in the Universe and we could see how this fits with the current status of observational cosmology.

[baric]

Of course, it would also logically mean that the majority of mass in the universe is contained within black holes!

 

Upon further thought, this may not be necessary. If the photons resulting from the matter-antimatter annihilation do not fully reflect the original mass (i.e. there was actual annihilation, rather than full conversion to energy), then the sum mass of the black holes does not need to be necessarily so large. It all depends on the ratio of matter annihilated to matter converted to energy.

Edited July 11, 2011 by baric

[ajb]

It all depends on the ratio of matter annihilated to matter converted to energy.

 

 

Behind the horizon? What about [math]E = mc^{2}[/math] ?

[baric]

Right, so for the rest of us outside we will never know what happened to the antimatter particle.

 

 

 

This sounds a bit naive. There is no mass loss if a particle and antiparticle collide behind the event horizon. In general relativity one takes mass and energy to be equivalent (well, it is all really much more complicated, but for a black hole this is fine). As an aside a black hole is only characterised by the mass, angular momentum and electric charge.

 

This is where I am unsure. In a matter-antimatter annihilation, is all matter fully converted or is a percentage of it actually annihilated (i.e. no resultant energy)?

 

What do you mean by this? One does expect physical black holes to be nearly electrically neutral in general.

 

What I mean is that, once the matter & antimatter have been converted to high-energy photons, then there ceases to be a distinction between them as long as they were within an EH. Although they are created traveling in opposite directions, their existence within an EH means they will be pulled back to the BH center regardless. There, they are just photons added to the overall mass of the BH.

 

In other words, a black hole maintains no distinction between matter and anti-matter. In this regard, it is neutral.

 

This is a prediction of your "theory". Indeed most of the mass of Universe does appear to be missing, see dark matter. Black holes and brown dwarfs make up what are known as MACHOs, that is Massive Compact Halo Objects. Current thinking is that MACHOs do not contribute significantly to dark matter. It is believed that non-baryonic dark matter is the dominant component of dark matter.

 

Right. In this scenario, the dark matter would be composed of black holes.

 

So, I think it is unlikely that your "theory" is consistent with observation, but one has to do the maths to show this. That is we would need to know the density of black holes you require in the Universe and we could see how this fits with the current status of observational cosmology.

 

I agree. I think first I need to better understand the matter-antimatter annihilation and establish an upper bound on the mass within black holes.

 

This is not really a theory as much as a line of speculation.

 

Behind the horizon? What about [math]E = mc^{2}[/math] ?

 

Right, my original assumption is that there is a full conversion to energy. That seems the most obvious. This makes the argument that the majority of mass in the universe would be bound within black holes, if this mechanism is responsible for the matter-antimatter disparity.

[ajb]

I agree. I think first I need to better understand the matter-antimatter annihilation and establish an upper bound on the mass within black holes.

 

I don't think you care about the annihilation process. Once the matter and antimatter has crossed the horizon (and this is a frame dependant statement) the no hair theorem comes into play. For us it means that as an outside observer we are not privy to what happens on the other side of the horizon. In some sense black holes do not care what they "eat" nor how they "digest" it!

 

A mechanism has been put forward by Hawking [1] in which the evaporation of primordial black holes could lead to baryon-antibaryon asymmetry. This does require grand unified theories that violate CP and baryon number conservation. So, black hole evaporation + GUT physics could explain the matter to antimatter ratio. This idea has been explored by other authors. So a good hunt through the literature is required.

 

References

 

[1] S. W. HAWKING. Black hole explosions? Nature 248, 30 - 31 (01 March 1974)

[baric]

I don't think you care about the annihilation process. Once the matter and antimatter has crossed the horizon (and this is a frame dependant statement) the no hair theorem comes into play. For us it means that as an outside observer we are not privy to what happens on the other side of the horizon. In some sense black holes do not care what they "eat" nor how they "digest" it!

 

Yes, I agree. So, in that sense, all matter drawn into black holes is effectively removed from the matter-antimatter balance.

 

This means that an expected probabilistic imbalance in early black hole formation (wherein more black holes formed from one type of matter than the other by chance) would necessarily lead to an observed imbalance in the matter-antimatter ratio across the remaining visible matter (visible = outside of any EH).

 

The remaining antimatter would be eventually dispersed into gamma radiation by outside-EH interactions with normal matter, exaggerating the perceived imbalance. In this case, you would not need a large amount of cosmic mass residing in black holes at all.

 

As an aside, I do believe that some theoretical work is being done on what happens within the EH.

[pantheory]

I was reading the latest issue of Astronomy today. There was a nice article on antimatter and a short article about a simulation with two neutron stars that merged into a black hole. Very interesting stuff, as usual!

 

I started thinking about the ramifications of anti-matter and black holes and wondered if the matter-antimatter assymetry could be explained by it.

 

For example, if an anti-matter particle enters an event horizon, it will produce a corresponding amount of high-energy photons when it inevitably collides with normal matter. However, these photons are trapped within the EH and ultimately increase the mass of the black hole as they are pulled back to its center. In other words, the mass loss from the matter-antimatter annihilation becomes moot if it occurs within an EH.

 

This means that black holes would be effectively neutral with regards to matter-antimatter and could therefore explain the antimatter imbalance.

 

Of course, it would also logically mean that the majority of mass in the universe is contained within black holes!

 

 

I am not a physicist nor an astronomer. Someone please explain where my thinking is flawed on this subject.

Hi baric,

 

This is Forrest Noble, hope all is well with you. I've seen very recent articles concerning fermilab's claim concerning possible asymmetry between protons and anti-protons, supposedly explaining why we see no anti-protons in the big picture of the universe. I hope they are right since I've been claiming/predicting asymmetry concerning anti-protons but not positrons vs. electrons , for maybe 30 years now or longer.

 

http://scienceblogs....atter_in_th.php

 

I also think this is the reason anti-protons are so difficult to store. Accordingly enforcing their spin by high speed acceleration or by cryogenics are the proven ways to extend there half-life which I consider to be like time dilation for any short lived particle. My expectation is that there life in the absence of matter is about the same as a free neutron, about 11 minutes in a low temp. vacuum. Even if their half life were much longer, like a thousand years for instance, or even a million years, that would explain why we see no anti-matter in the universe as a whole. We, however, see many positrons (via their annihilation) surrounding the central black hole in our galaxy.

Edited July 12, 2011 by pantheory

[csmyth3025]

...This means that an expected probabilistic imbalance in early black hole formation (wherein more black holes formed from one type of matter than the other by chance) would necessarily lead to an observed imbalance in the matter-antimatter ratio across the remaining visible matter (visible = outside of any EH).

 

The remaining antimatter would be eventually dispersed into gamma radiation by outside-EH interactions with normal matter, exaggerating the perceived imbalance. In this case, you would not need a large amount of cosmic mass residing in black holes at all...

I'm not knowledgeable enough about cosmology to comment directly on the plausibility of your speculation. There are several speculative explanations being offered for the observed baryon asymmetry that are presented in the Wikipedia article on the subject:

http://en.wikipedia....aryon_asymmetry

 

The main problem with your speculation is that you're substituting one mysterious mechanism for baryon asymmetry (the proposed preference of black holes to absorb anti-matter over regular matter) for other equally mysterious and unexplained mechanisms such as CP symmetry violation.

 

An interesting pie chart that illustrates the magnitude of the problem can be found on the NASA webpage here:

http://map.gsfc.nasa...0998/index.html

 

Content of the Universe - Pie Chart

 

WMAP data reveals that its contents include 4.6% atoms, the building blocks of stars and planets. Dark matter comprises 23% of the universe. This matter, different from atoms, does not emit or absorb light. It has only been detected indirectly by its gravity. 72% of the universe, is composed of "dark energy", that acts as a sort of an anti-gravity. This energy, distinct from dark matter, is responsible for the present-day acceleration of the universal expansion. WMAP data is accurate to two digits, so the total of these numbers is not 100%. This reflects the current limits of WMAP's ability to define Dark Matter and Dark Energy.

 

Credit: NASA / WMAP Science Team

 

 

At first glance it would seem that since "only" 4.6% of all the matter/energy thought to exist is in the form of ordinary matter, there might be another 4.6 % of anti-matter that has been preferentially swallowed up by black holes. You have to consider, though, that this 4.6% represents all of the stars and galaxies and all of the inter- and intra- galactic gas and dust we can see or reasonably infer. That's a lot of black holes.

 

Chris

[ajb]

This means that an expected probabilistic imbalance in early black hole formation (wherein more black holes formed from one type of matter than the other by chance) would necessarily lead to an observed imbalance in the matter-antimatter ratio across the remaining visible matter (visible = outside of any EH).

 

The trouble is that I cannot imagine that it was just by chance that early black holes "gobbled up" more antimatter than matter. If initially there was equal parts of matter and antimatter then why would we expect antimatter to be favoured over matter? It is true that you do not need a large amount of asymmetry, but still I don't think that chance is sufficient.

 

Unless you put some mechanism for the asymmetry I am sure that any statistical model here would give that baryons and antibaryons form black holes or are "eaten" by black holes at the same rate.

 

It could be that high energy physics (GUT scale or even quantum gravity) has this asymmetry (violates CP) and this is important for the physics of these early black holes. But it looks like you have not really solved the asymmetry as you need to figure out why gravity (+ GUT physics) does not treat matter and antimatter equally.

 

Hawking's idea about the primordial black hole evaporation being the cause of the asymmetry also requires CP violations in the GUT physics.

[baric]

The trouble is that I cannot imagine that it was just by chance that early black holes "gobbled up" more antimatter than matter. If initially there was equal parts of matter and antimatter then why would we expect antimatter to be favoured over matter? It is true that you do not need a large amount of asymmetry, but still I don't think that chance is sufficient.

 

If there is probabilistic behavior in the universe, then it is inevitable that one form of matter is consumed at a greater rate than others. Not by preference, but simply by chance. This, imo, is a seed for an imbalance that may ultimately mean nothing at all

[pantheory]

deleted double posting

Edited July 12, 2011 by pantheory

[csmyth3025]

If there is probabilistic behavior in the universe, then it is inevitable that one form of matter is consumed at a greater rate than others. Not by preference, but simply by chance. This, imo, is a seed for an imbalance that may ultimately mean nothing at all

I don't understand your reasoning. As far as I know, probabilistic behavior doesn't require that one reaction is preferred over another. Please explain or provide a link.

 

Chris

[baric]

I don't understand your reasoning. As far as I know, probabilistic behavior doesn't require that one reaction is preferred over another. Please explain or provide a link.

 

Chris

 

I specifically said it was not by preference, but chance. I'm not sure how to explain something I didn't say or don't believe.

[csmyth3025]

...If there is probabilistic behavior in the universe, then it is inevitable that one form of matter is consumed at a greater rate than others...

Let me try to more clearly restate my question: Why is it inevitable that one form of matter is consumed at a greater rate than others if there is probabilistic behavior in the universe?

 

I consider tossing a coin in the air to be an example of probabilistic behavior. Your statement sounds to me like: "If a tossed coin exhibits probabilistic behavior, then it is inevitable that heads will come up more often than tails."

Chris

[ajb]

I consider tossing a coin in the air to be an example of probabilistic behavior. Your statement sounds to me like: "If a tossed coin exhibits probabilistic behavior, then it is inevitable that heads will come up more often than tails."

 

I think the point is that in an experiment consisting of a finite number of tosses then you will have 1) equal number of heads or tails (need an even number of tosses) or 2) more heads than tails or more tails than heads.

 

But in the context of the theory being proposed it seems that it was just luck that decided more matter than antimatter. This I think will be very difficult to really get your head around.

[baric]

I consider tossing a coin in the air to be an example of probabilistic behavior. Your statement sounds to me like: "If a tossed coin exhibits probabilistic behavior, then it is inevitable that heads will come up more often than tails."

Chris

 

Which is a true statement. It is also inevitable that tails will come up more often than heads.

 

In fact, if you flipped a coin an large number of times, you would find that the chance that "heads = tails" quickly becomes infinitesimal since the chance decreases in a factorial manner.

 

Remember, probability theory estimates discrete behavior, it does not predict it.

 

So, my question boils down to this...

 

If, as an expected result of probabilistic behavior, one form of matter was disproportionately prevented from interacting with the rest of the universe (by virtue of being inside an EH), what effect would this imbalance have on the remaining matter?

 

If the "outside of an EH" universe reached a 51-49 matter-antimatter balance, would this imbalance persist, or would we eventually be left with a 2-0 imbalance with a lot of gamma radiation?

 

But in the context of the theory being proposed it seems that it was just luck that decided more matter than antimatter. This I think will be very difficult to really get your head around.

 

Hang on... it's not luck.

 

'Anti-matter' is just our descriptive label for the less frequent form of matter. No matter how the imbalance played out, the word "anti-matter" would be used in the same fashion.

 

Also, this is not really a theory. It's just an idea I'm trying to poke holes in.

Edited July 13, 2011 by baric

[csmyth3025]

Which is a true statement. It is also inevitable that tails will come up more often than heads.

 

In fact, if you flipped a coin an large number of times, you would find that the chance that "heads = tails" quickly becomes infinitesimal since the chance decreases in a factorial manner.

 

Remember, probability theory estimates discrete behavior, it does not predict it.

 

So, my question boils down to this...

 

If, as an expected result of probabilistic behavior, one form of matter was disproportionately prevented from interacting with the rest of the universe (by virtue of being inside an EH), what effect would this imbalance have on the remaining matter?

 

If the "outside of an EH" universe reached a 51-49 matter-antimatter balance, would this imbalance persist, or would we eventually be left with a 2-0 imbalance with a lot of gamma radiation?

 

 

 

Hang on... it's not luck.

 

'Anti-matter' is just our descriptive label for the less frequent form of matter. No matter how the imbalance played out, the word "anti-matter" would be used in the same fashion.

 

Also, this is not really a theory. It's just an idea I'm trying to poke holes in.

(bold added by me)

 

I'm no expert on probability theory. I'm relying on the following passage to predict that a large number of interactions will show virtually no preference toward one interaction over another:

 

According to the law of large numbers, if a large number of dice are rolled, the average of their values (sometimes called the sample mean) is likely to be close to 3.5, with the accuracy increasing as more dice are rolled.

 

It follows from the law of large numbers that the empirical probability of success in a series of Bernoulli trials will converge to the theoretical probability. For a Bernoulli random variable, the expected value is the theoretical probability of success, and the average of n such variables (assuming they are i.i.d.) is precisely the relative frequency.

 

For example, a fair coin toss is a Bernoulli trial. When a fair coin is flipped once, the theoretical probability that the outcome will be heads is equal to 1/2. Therefore, according to the law of large numbers, the proportion of heads in a "large" number of coin flips "should be" roughly 1/2. In particular, the proportion of heads after n flips will almost surely converge to 1/2 as n approaches infinity.

(ref. http://en.wikipedia....f_large_numbers )

 

You're proposing a precondition (the preferential absorption of anti-matter by primordial black holes) that is just as speculative as any other explanation that might result in the observed disparity between matter (which is ubiquitous) and anti-matter (which is almost non-existent).

 

As far as I know there is no evidence to support this speculative assumption.

 

Chris

[baric]

(bold added by me)

 

I'm no expert on probability theory. I'm relying on the following passage to predict that a large number of interactions will show virtually no preference toward one interaction over another:

 

I never said there would be a preference! However, the odds of parity diminish with an increased number of interactions even as the the average converges towards it.

 

You're proposing a precondition (the preferential absorption of anti-matter by primordial black holes) that is just as speculative as any other explanation that might result in the observed disparity between matter (which is ubiquitous) and anti-matter (which is almost non-existent).

 

As far as I know there is no evidence to support this speculative assumption.

 

Chris

 

As I have said multiple times, there would be no preference towards one type of matter over the other. However, mathematically it is inevitable that one type of matter would be absorbed in a greater quantity, by random chance alone.

[csmyth3025]

I never said there would be a preference! However, the odds of parity diminish with an increased number of interactions even as the the average converges towards it.

 

 

 

As I have said multiple times, there would be no preference towards one type of matter over the other. However, mathematically it is inevitable that one type of matter would be absorbed in a greater quantity, by random chance alone.

 

"...However, the odds of parity diminish with an increased number of interactions even as the the average converges towards it..."

 

Is this part of the theory of large numbers? Can you provide a proof for this statement - or a link that contains such a proof?

 

Chris

[baric]

"...However, the odds of parity diminish with an increased number of interactions even as the the average converges towards it..."

 

Is this part of the theory of large numbers? Can you provide a proof for this statement - or a link that contains such a proof?

 

Chris

 

It is mathematically demonstrable and is probably too trivial to be considered part of the theory.

 

Given an odd number of interactions, there is a 0% chance of parity regardless of the number of interactions, so we can safely ignore those.

 

For an even number of interactions, the chance of parity (for a 50/50 chance like the selection between two equal choices) is:

 

p = ((n/2)! * (n/2)!) / n!

 

 

So, for values of n, p(n) =

 

p(2) = 1/2

p(4) = 1/6

p(6) = 1/20

p(8) = 1/70

p(10) = 1/252

...

 

 

I hope that makes sense.

Edited July 17, 2011 by baric

[csmyth3025]

It is mathematically demonstrable and is probably too trivial to be considered part of the theory.

 

Given an odd number of interactions, there is a 0% chance of parity regardless of the number of interactions, so we can safely ignore those.

 

For an even number of interactions, the chance of parity (for a 50/50 chance like the selection between two equal choices) is:

 

p = ((n/2)! * (n/2)!) / n!

 

 

So, for values of n, p(n) =

 

p(2) = 1/2

p(4) = 1/6

p(6) = 1/20

p(8) = 1/70

p(10) = 1/252

...

 

 

I hope that makes sense.

Is this the basic idea (absolute difference)?

 

http://demonstration...teFrequencyOfC/

 

Chris

[baric]

Is this the basic idea (absolute difference)?

 

http://demonstration...teFrequencyOfC/

 

Chris

 

 

Yes, exactly. The absolute difference displayed on the left side would represent the matter-antimatter imbalance at any given time as caused by movement to within event horizons.

 

I am not saying that this is necessarily a significant observation! All I am pointing out is that this should occur and that there would be some expected matter-antimatter imbalance as a result of this random selection mechanism. I then wonder what kind of effect this would have, if any, on an early, dense universe. Would this difference become magnified, or would it simply average out over time?

 

Unlike the metaphorical coin toss, after all, these interactions do not represent independent events. Because of the matter-antimatter interaction, sequestering one form in a larger quantity could conceivably have ripple effects.