PPS The link in my post #37 to Harrison's free online text also has a complete treatment of vacuum Kerr-Newmann black holes in Chapter 9.
PPS The link in my post #37 to Harrison's free online text also has a complete treatment of vacuum Kerr-Newmann black holes in Chapter 9.
chas53 (06-21-2013),Glitch (06-21-2013),kencrowder (06-21-2013),Seeker725 (06-21-2013)
As a mental exercise I decided to calculate the speed an Earth-sized planet would have to move to stay in orbit around a singularity just inside the Event Horizon. For this exercise I used the supermassive black hole at the center of the Milky Way, which is estimated to be ~4 million solar masses.
Schwarzschild Radius (Event Horizon) = 2Gm/c^{2}Where:
Constant G = 6.67384E-11 (m/kg)^{2}
Milky Way Super Massive Black Hole Mass (m) = 7.956E+36 kg
Speed of Light (c) = 299,792,458 m/s
That would put the event horizon at 11,815,691,814 km (7,341,930,510 miles), or ~79 AU from the singularity. If we put an Earth-sized planet 78 AU from the singularity (just inside the Event Horizon) it would need to orbit the singularity at 2.2% the speed of light, or 6,595,434 m/s (14,753,566 mph), just to stay in orbit around the singularity. At that distance and speed the planet would make a complete orbit around the singularity every 126 days.
Last edited by Glitch; 06-30-2013 at 09:54 PM.
kencrowder (06-30-2013),njjmfm (07-02-2013),not_Fritz_Argelander (06-30-2013)
astroval (07-01-2013),chas53 (06-30-2013),Glitch (07-01-2013),kencrowder (06-30-2013)
not_Fritz_Argelander (07-01-2013)
For "simple" Schwarzschild black hole the "space-time fall" to the singularity is too strong, so there are no stable orbits.
But “simple” Schwarzschild black hole is exception. Rotating and charged black hole singularity not a point in the center, it is ring, and there is also second inner horizon.
As result inside inner Cauchy horizon stable orbits are exist. The form of stable orbits is a little bit complicated.
http://arxiv.org/pdf/1103.6140v4.pdf
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chas53 (07-01-2013),Glitch (07-01-2013),kencrowder (07-11-2013),not_Fritz_Argelander (07-01-2013)
Can massless BH be a charged one? I'm thinking that if their was points of extreme cold at the Hadron Epoch as well as the extreme 10,000,000,000,000K temperaures, it would act as a superconductor. With a temperature that high, the cold temperature would not necessarily be a -ve number.
Meade 12"
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Glitch (07-11-2013),not_Fritz_Argelander (07-11-2013)
You can't have a "massless" black hole. You can have a matter-less black hole or a vacuum black hole. But all black holes have mass.
If it isn't spinning it's a Reissner-Nordstrom black hole.
Reissner
If it spins, and is charged, it is a Kerr-Newman black hole.
Kerr
astroval (07-11-2013),chas53 (07-12-2013),Glitch (07-11-2013),kencrowder (07-11-2013)
From my limited understanding of string theory, there can be charged massless black holes, but only in pairs (oppositely charged). A black hole can only be massless when measured from infinity. At finite distances they would be white holes and have a repulsive force. Although, the paper referenced below suggests that a four-dimensional black hole may become massless.
"After Calabi-Yau compactification these may wrap around minimal two (three) surfaces and appear as four-dimensional black holes. As the area of the surfaces around which they wrap goes to zero, the corresponding black holes become massless."
I am sure not_Fritz_Argelander can explain it better, you are getting beyond my pay grade.
Sources:
Massless Black Holes and Conifolds in String Theory
Massless Black Hole Pairs in String Theory
astroval (07-12-2013),not_Fritz_Argelander (07-11-2013)
I'm not sure that I believe in these calculations / predictions. I think that since both papers rely on real manifolds they may not be physically relevant at the small length scales involved. Even assuming the computations are correct, the interpretation of the solutions as implying zero mass black holes is suspect. The nagging doubt in the back of my mind is whether string theories on a space-time manifold with coordinates in the real numbers is a sane way to do physics. I suspect not.
Renormalization is used as a technique rather prominently in the first paper. Renormalization - Wikipedia, the free encyclopedia
While undeniably useful in condensed matter physics where natural cutoffs suggest themselves, the need to resort to renormalization methods to avoid divergences is something that can also be considered a symptom. The early motivation for dual-resonance theories (ancestral to string theories) was partly dissatisfaction with renormalization techniques applied to point particles.
Dual resonance model - Wikipedia, the free encyclopedia
I think that the causal set approach is more consistently principled. It also illustrates an alternative to having a manifold with real coordinates.
Causal sets - Wikipedia, the free encyclopedia
The continuous real manifold in the space time continuum may well be only an approximation to a granular structure at small length scales. So calculations based on a continuous structure at all length scales may be shown to be irrelevant.
astroval (07-12-2013),chas53 (07-12-2013),Glitch (07-11-2013),kencrowder (07-11-2013)
My understanding of string theory is introductory, at best. I have enough difficulty getting my head around non-Euclidean geometry of quantum mechanics, but I find it far easier to understand than the eleven dimension multiverse postulated by string theory. People a lot smarter than I have embraced string theory as a possible explanation for unification, including Stephen Hawkings, so there must be something to it. When you get into four dimensional manifolds and how this can violate Newton's law of conservation of momentum, my brain begins to hurt.
astroval (07-12-2013),kencrowder (07-12-2013)