Various varieties of black holes

[DiracPool]

Here's a quote by Modred from another thread:

https://www.physicsforums.com/showthread.php?t=683377

Blackholes evaperation is an incredibly slow process, for a Schwarzschild black hole of 1 solar mass
the evaperation process by Hawking radiation is 10^67 years. Thats for an uncharged non rotating black hole.

My question isn't about the Hawking radiation part of the statement, its about the "uncharged non-rotating black hole" part. how do we know if a black hole is charged, what it's charge is, and if it is rotating and how much. I thought a black hole was a singularity. How can a singularity have charge and rotate or not rotate? If you have gotten this far with an explanation, then please tell me the factors or variables that lead a black to be charged or not, or to spin or not.

 

[WannabeNewton]

A black hole is not a singularity by any means; I'm not sure where you read that. One stationary electrovacuum exact black hole solution with charge and angular momentum is the Kerr Newman metric. The Kerr metric, Schwarzschild metric, and Nordstrom metric are all special case of this one. In order to tell if such a black hole solution has charge or angular momentum you can simply look at the standard forms of the metrics for the respective solutions and see which parameters are zero and which aren't. For example, for Schwarzschild black holes, both the angular momentum parameter $J$ and charge $Q$ will be zero. For the Nordstrom metric the angular momentum $J$ will vanish but the charge $Q$ of the black hole will not (such a black hole will act as a spherically symmetric static charge distribution). For the Kerr metric the angular momentum $J$ won't vanish but the charge $Q$ will and so on. In my experience, most of the details are quite mathematical.

Whether or not a black hole becomes charged or rotating depends crucially on the nature of the gravitational collapse and the bodies involved in the collapse that leads to its formation.

See here for more details: http://en.wikipedia.org/wiki/Kerr_Newman_metric#Special_cases_and_generalizations

http://en.wikipedia.org/wiki/Rotating_black_hole#Formation

 

[Naty1]

I thought a black hole was a singularity. How can a singularity have charge and rotate or not rotate? If you have gotten this far with an explanation, then please tell me the factors or variables that lead a black to be charged or not, or to spin or not.

There is an unknown unobservable entity at the center of a black hole...the singularity...where equations diverge and so are thought not to be good descriptions. All we know is that gravitational curvature becomes extreme. But the perspective from GR tells us that what is observed from outside where we reside, are the characteristics of the matter-energy in the past lightcone from the collapse...and any subsequent infalling matter-energy. We cannot observe anything inside the horizon.

An alternative view was originated by Leonard Susskind via Black Hole Complementarity and the Holographic Principle. In these views all the characteristics of the infalling matter energy appear on a stretched horizon about a Planck length outside the event horizon. Information is 'smeared' across the horizon by infalling matter-energy. From these considerations Susskind eventually convinced Hawking that information is not lost in a black hole...eventually, by time of the death [collapse] of the BH, the information which has 'disappeared' is returned via scrambled Hawking radiation. Meantime, all that is observable falls under the 'no hair theorem'...charge,mass, angular momentum.

A perfectly symmetric collapse leads to no spin. I am not positive but a star might collapse that way. My impression is a collapse of stellar dust is less likely to collapse without spin. There are maximum limits on spin.

 

[phyzguy]

From an astrophysical standpoint, it is believed that most real black holes are uncharged. This is because, if they are charged, they rapidly attract enough of the opposite charge from the background plasma in the universe to discharge them. However, most astrophysical black holes appear to be rotating, and many of them are rotating near the maximum possible limit. See, for example, this link.

 

[Mordred]

I can't recall where I read it, so cannot state the reliability of the source. However I heard or read somewhere that rotating black holes will tend to become non rotating? Is that true or not?

edit found the reference

Thus, in a way fully analogous to the Penrose process for particles (18), one may say that if the
energy at infinity increases because the black hole absorbed negative-at-infinity energy, then the
black hole rotation must also slow down by absorbing matter with negative angular momentum.
Blandford and Znajek [49] made the brilliant discovery that an electromagnetic form of the
Penrose process may work. In their model, the energy for the jet is extracted from the spin energy
of the black hole via a torque provided by magnetic field lines that thread the event horizon

section 121 page 45/91

http://arxiv.org/abs/1104.5499

 

[Mordred]

If your interested Diracpool here is an article that shows Hawking radiation in the main types of Black holes. Although its not an easy read. he main gist to gather from the article is that the Hawking radiation given by the form

$$T = \frac{\hbar c^3}{8 \pi k G M}$$

is applicable on the Schwartzchild non-rotating, uncharged case. Other factors come into play on other BH types.

http://arxiv.org/pdf/gr-qc/0010055v1.pdf

 

[Naty1]

Mordred:

However I heard or read somewhere that rotating black holes will tend to become non rotating?

Rotating BH WITH accretion disk interactions. In other words, sounds like external matter-energy is required. If interested enough, you may want to read all the qualifiers that follow your quote. I have my doubts about the 'Penrose process' but the last sentence of your quote is the type I have seen elsewhere. Seems like a LOT of uncertainty remains...according to the authors...Or maybe they are treading politically sensitive waters [fluids]... [that's a hydrodynamic joke!]

On page 3 I found this description which sure sounds very different from the page 40 you
posted.

] The radiation we receive from quasars and microquasars comes not from the black holes themselves, but instead originates in the accretion disks which surround them. In these accretion disks, angular momentum is gradually removed by some presumably (although not necessarily dissipative process, causing matter to spiral down into the black hole, converting its gravitational energy into heat, and then, by various processes, radiating this energy. The radiation subsequently leaks through the disk, escapes from its surface, and travels along trajectories curved (in space) by the strong gravity of the black hole, eventually reaching our telescopes.

and Pg 68 concluding remarks:

...despite their prominent role in nature... out flows are not accounted for in any of the four main accretion models we presented, as the models all assume that the accretion rate is constant with radius. In reality, out flows may be triggered by any of three mechanisms: thermal, radiative, or centrifugal. ...

That's a staggering comment! I wonder if those three triggers only apply when an accretion disk is present? I can imagine an isolated BH NOT comoving with the CMBR absorbing radiation non symmetrically...but it sounds like their entire analysis is based on accretion disk- BH interactions...

Interesting read...

 

[Mordred]

goes even further than that in that, one section shows a possible method of identifying whether a BH has a solid core or singularity type structure. Ie neutron vs BH event horizon argument that often crops up.

On the statement I posted it sounds like the accretion jet is a source of loss of BH rotation via the magnetic torque interaction. However as you pointed out their are other angular momentum factors in each accretion disk zone. Some are transferred, some are lost. The article is a good read but hard to square away all the processes it describes.here4

Just prior to that quote and I should have concluded it was the WALD argument against the Penrose process, not sure the final result of that other than this paper. its in section 119 or 120. I have zero familiarity with it other than the Penrose particle production process. Which is also in the article

Edit: In a way it makes sense in that the accretion disk does have an energy-mass density, therefore it would have a local gravitational influence on the central BH. I cannot see how it wouldn't

 

[WannabeNewton]

The Penrose process does reduce the angular momentum of a rotating black hole. There is a wave analogue called superradiance which does the same. See section 12.4 of Wald and problem 12.5b of Wald (I'm still trying to solve problem 12.5b xP).

 

[Mordred]

Thanks for that clarification , currently on phone got to love field work. I'll look again at that section later on

 

[Lino]

... How can a singularity have charge and rotate or not rotate? ...

DiracPool, Ignoring the BH versus singularity issue, I think the point is that when some one / paper / calculation is making a general statement, it is not possible to determine if it is applicable to a specific BH - maybe it is charged / rotating, maybe it isn't. Therefore an assumption is made in order to facilitate the working / discussion, thus avoiding the "... what if the BH is rotating in the opposite direction ..." side tracks. It's kinda like having a general conversation about bicycles and assuming that the bikes that your are talking about have working brakes, without knowing if the brakes are working on a specific bike.

(I'm not an expert myself, but this is the way that I read these types of things.)