Black Holes: growth affected by Higgs or Dark energy/matter

[JustinLevy]

I am curious to what extent black hole growth can be used to probe understanding of various particles/fields.

1] Dark matter:
Let's consider dark matter to be so weakly interacting we can model it as a perfectly non-interacting gas. For even more simplification, let's assume dark matter particles have some thermal equilibrium distribution. (Are these simplifications unappropriate?) So dark matter will then only settle into gravitational wells to the extent that its thermal distribution will allow. So no "clumping", but definitely more dark matter in a galaxy well than in intergalactic space.

Now, if we place a black hole into this gas, all dark matter particles without enough thermal energy to orbit or escape will be eventually consumed. However, since the gas is non-interacting, it can't "bump" other dark matter particles on its way it. So this consuming could be incredibly slow, and self limiting in that many dark matter particles in the galaxy just won't be consumed at all. In this non-interacting limit, it seems dark matter would be slowly "cleaned" from the area by a black hole. Overall leaving the gas slightly hotter than before (since it preferentially devoured the low energy particles).

This process however would have to repeat when galaxies collide. Since the gas consumption is a non-equilibrium process, I'm not sure how to estimate its speed. I also don't know the differential sensitivity of black hole mass measurements in astronomy (maybe wrong word, but what I mean is I don't care about the absolute value as much as how the value changes in time). Can anyone give estimates or insight on whether these effects could be measureable?

Also, if dark matter does self-interact, the growth rate would be even larger. So could black hole growth be used to place limits on dark matter interactions?


2] Higgs
It seems most particle physics measurements are sensitive to the vacuum expectation value, and not the overall energy density of the Higgs. But since it is the vacuum itself (instead of "particles"/excitations) that has this energy density of the Higgs, then the black holes clearing out the region of dark matter particles cannot apply here for the Higgs. It seems the black hole would have to be pulling in extra energy at a rate proportional to its area and the Higgs energy density. Could black hole mass growth be used to therefore place a limit on the Higgs energy density, using current measurements of the higgs vev from particles physics?

3] Dark energy / Cosmological constant
If the accelerated universe expansion is due to a physical field with positive energy density and negative pressure, then it seems GR would dictate that this energy would fall into a black hole along with a free falling observer. This is in contrast to accelerated universe expansion due to a positive cosmological constant, which is just a constant of the universe and not a physical energy density which can fall into a black hole, so the black hole will not grow. Is this logic correct, and could black hole growth (in principle at least) allow one to distinguish between dark energy and a cosmological constant?

 

[Q-reeus]

...3] Dark energy / Cosmological constant
If the accelerated universe expansion is due to a physical field with positive energy density and negative pressure, then it seems GR would dictate that this energy would fall into a black hole along with a free falling observer. This is in contrast to accelerated universe expansion due to a positive cosmological constant, which is just a constant of the universe and not a physical energy density which can fall into a black hole, so the black hole will not grow. Is this logic correct, and could black hole growth (in principle at least) allow one to distinguish between dark energy and a cosmological constant?

Great questions, but just on 3], your idea that a positive CC doesn't imply a positive energy density is not right. From http://en.wikipedia.org/wiki/Dark_energy, opening paragraphs:

"In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe.[1] Dark energy is the most accepted theory to explain recent observations and experiments that the universe appears to be expanding at an accelerating rate. In the standard model of cosmology, dark energy currently accounts for 73% of the total mass-energy of the universe.[2]

Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously,[3] and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space. Contributions from scalar fields that are constant in space are usually also included in the cosmological constant. The cosmological constant is physically equivalent to vacuum energy. Scalar fields which do change in space can be difficult to distinguish from a cosmological constant because the change may be extremely slow."

So whatever you wish to label it, positive energy density and negative pressure are always assumed. It's been my thinking for some time that DE should indeed be streaming into notional BH's (or as I prefer to think, GCO's - 'gravitationally collapsed objects'), making the talk of evaporation from Hawking Radiation a joke. For any BH/GCO of typically solar mass or greater, just the opposite is surely implied by DE and overwhelmingly so by many orders of magnitude. Yet have seen no talk of this. Wondering why. Perhaps the notion of BH's growing forever at an increasing rate is an embarrassment that has paradoxical implications.

EDIT: Just came across a link to such a paper: http://arxiv.org/pdf/0803.2005v1 - so they do exist after all.
Not sure if this one is regarded as 'mainstream' though. It may be that in standard GTR treatment, energy density and pressure somehow formally cancel re gravitational mass change for in-falling DE - needs some expert opinion.

Further study: From the Wikipedia link on DE sited earlier:
"The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate. The reason why a cosmological constant has negative pressure can be seen from classical thermodynamics; Energy must be lost from inside a container to do work on the container. A change in volume dV requires work done equal to a change of energy −p dV, where p is the pressure. But the amount of energy in a box of vacuum energy actually increases when the volume increases (dV is positive), because the energy is equal to ρV, where ρ (rho) is the energy density of the cosmological constant. Therefore, p is negative and, in fact, p = −ρ." This is the standard situation.

Now, in the article linked from http://arxiv.org/pdf/0803.2005v1, there is:
dM/dt = 4πAM²(p + ρ) - (5), so for a 'standard' CC, it follows that pressure and energy density do indeed cancel out. It is for deviations from standard that growth or otherwise is the main consideration in that paper.

 

[JustinLevy]

Great questions, but just on 3], your idea that a positive CC doesn't imply a positive energy density is not right.

Yes, whether a physical field or a cosmological constant, they will both have a term with that same units. But there is a difference between a physical field (like in a quintessence model) and a cosmological constant.

For example, a black hole solution with a positive cosmological constant, the mass of the black hole is not increasing with time. The black hole doesn't gain mass by "absorbing" space that had a positive cosmological constant or something.

So despite the units being the same, I think my dynamical distinction between the two should still hold. I of course could be wrong, but I wanted to attempt a clarification, since I don't think the wikipedia section you quoted contradicts what I was trying to convey.

However, from your additional information you provided in the edit, it sounds like if the negative pressure from whatever is dark energy happens to have the equation of state that p=-rho, then a black hole still couldn't gain mass on it? That seems a bit strange to me. But I guess I shouldn't underestimate the non-intuitiveness of negative pressure. I'll check out that paper. Thanks!


Does anyone else have comments to add?
How about the Higgs or Dark Matter?

 

[Q-reeus]

Yes, whether a physical field or a cosmological constant, they will both have a term with that same units. But there is a difference between a physical field (like in a quintessence model) and a cosmological constant.

A matter of definition perhaps. As per that Wiki article, CC is a 'catch all' in a sense - could represent vacuum energy or a scalar field such as quintessence, provided it can be considered time invariant (hence the 'constant' part in cosmological).

However, from your additional information you provided in the edit, it sounds like if the negative pressure from whatever is dark energy happens to have the equation of state that p=-rho, then a black hole still couldn't gain mass on it? That seems a bit strange to me.

To me too. For a long time was puzzled how pressure 'all by itself' (distinct from the hydrodynamic stress energy density such pressure induces in matter) could be a source of gravitation. But it's there in the energy-momentum stress tensor as source terms: http://en.wikipedia.org/wiki/Stress–energy_tensor. I wasn't at all sure this could be directly applied to DE, but will defer to experts that know the game, and that aint me. Some papers that go into the role of pressure/stress in GR: http://arxiv.org/abs/gr-qc/0510041, http://arxiv.org/abs/gr-qc/0505040 Could be wrong but the present status of that equation of state p = −ρ seems to be a purely mathematical concoction that neatly balances the need to explain flatness and accelerated expansion simultaneously. Hence DE nearly always labeled 'mysterious'.

...How about the Higgs or Dark Matter?

Way out of my league. Only comment is re the dark matter halo's as non-interacting gas - have you looked at how gravitational perturbation from eg. stars may effect the dynamics of 'swallow time'?