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			<title>the gluon</title>
			<link>http://www.physicsforums.com/blog.php?b=530</link>
			<pubDate>Sat, 22 Nov 2008 15:50:04 GMT</pubDate>
			<description>1 eV = 1.602e-19 joules  (joules/c^2 = kg) 
 
 
Properties of the gluon (g)- 
 
neutron mass- 939.566 MeV/c^2 (1.675e-27 kg) 
 
up quark mass- ~2.4 MeV/c^2 (1.5 - 3.3) 
 
down quark mass- ~4.75...</description>
			<content:encoded><![CDATA[<div>1 eV = 1.602e-19 joules  (joules/c^2 = kg)<br />
<br />
<br />
Properties of the gluon (g)-<br />
<br />
neutron mass- 939.566 MeV/c^2 (1.675e-27 kg)<br />
<br />
up quark mass- ~2.4 MeV/c^2 (1.5 - 3.3)<br />
<br />
down quark mass- ~4.75 MeV/c^2 (3.5 - 6.0)<br />
<br />
energy unaccounted for by mass- 940 - (2 x 4.75 + 2.4) &#8776; 928 MeV/c^2<br />
<br />
928/3 = ~gluon energy (~309 MeV)<br />
<br />
The gluon is considered massless (or at least &lt;20 MeV) so it would appear that its energy can only come about from momentum (it also has spin 1 which means it is a boson and similar to a photon, except that it mediates strong colour charge).<br />
<br />
<br />
From Einstein's equation-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'e=pc')"><img src="latex_images/preview0-4.png" border=0 align=top alt='LaTeX Code: e=pc '></a><br />
<br />
where p is momentum and c is the speed of light.<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'e=\\frac{hc}{\\lambda}\\ \\ \\ \\ \\text{where}\\ \\ p=\\frac{h}{\\lambda}')"><img src="latex_images/preview0-5.png" border=0 align=top alt='LaTeX Code: e=\\frac{hc}{\\lambda}\\ \\ \\ \\ \\text{where}\\ \\ p=\\frac{h}{\\lambda} '></a><br />
<br />
&#955; is wavelength<br />
<br />
Therefore<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\lambda=\\frac{hc}{e}')"><img src="latex_images/preview0-6.png" border=0 align=top alt='LaTeX Code: \\lambda=\\frac{hc}{e} '></a><br />
<br />
based on e = 309 MeV = 4.950e-11 joules, <br />
<br />
&#955; = 4.013e-15 m<br />
<br />
or 4 fm (1 fm = 1e-15 m). Considering that quarks are approx 1.3 fm apart, this would mean one gluon wavelength approx. equals one complete circuit of all three quarks.<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'f=\\frac{c}{\\lambda}\\equiv \\frac{e}{h}')"><img src="latex_images/preview0-7.png" border=0 align=top alt='LaTeX Code: f=\\frac{c}{\\lambda}\\equiv \\frac{e}{h} '></a><br />
<br />
where f is frequency<br />
<br />
f = 7.471e22 Hz<br />
<br />
Gamma rays are approx 300e18 Hz at 1.24 MeV (frequencies as high as 2.9e27 Hz, &#955; = 1e-19 m, have been detected from astrophysical sources) which means the gluon might be described as a high energy gamma ray that carries colour charge.<br />
<br />
<br />
The frequency of the gluon appears to increase as the hadron becomes more massive (but still more or less staying within the same order). The increase in mass also introduces heavier quarks-<br />
<br />
strange quark mass- ~100 MeV/c^2 (70 - 130)<br />
<br />
charmed quark mass- ~1.25 GeV/c^2 (1.16 - 1.34)<br />
<br />
bottom quark mass- ~4.25 GeV/c^2 (4.13 - 4.37)<br />
<br />
<br />
neutron (udd)- 939.566 MeV (-2.4-2x4.75) =&gt; ~928/3 = 309 MeV gluon energy<br />
<br />
Sigma (uus)- 1189.37 MeV =&gt; ~362 MeV g<br />
<br />
charmed sigma (uuc)- 2454 MeV =&gt; ~400 MeV g<br />
<br />
charmed omega (ssc)- 2697.5 MeV =&gt; ~416 MeV g<br />
<br />
bottom sigma (uub)- 5807.8 MeV =&gt; ~518 MeV g<br />
<br />
bottom omega (ssb)- 6165 MeV =&gt; ~572 MeV g<br />
<br />
there are a couple of blips where the energy drops (e.g. double charmed xi (dcc)- 3519 MeV, g=338 MeV) but generally, it appears the energy of the gluon increases as the mass of the hadron increases. <br />
<br />
This might go some way to explaining the massive gamma ray bursts that are suppose to occur during quark-novae (i.e. energy released in the region of 10^46 joules, the equivalent of ~60 Jupiters), possibly brought on by quark deconfinement.<br />
<br />
<br />
sources-<br />
<a href="http://en.wikipedia.org/wiki/Gluon" target="_blank">http://en.wikipedia.org/wiki/Gluon</a> <br />
<a href="http://en.wikipedia.org/wiki/List_of_baryons" target="_blank">http://en.wikipedia.org/wiki/List_of_baryons</a></div>

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			<dc:creator>stevebd1</dc:creator>
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			<title>… boundary calculations …</title>
			<link>http://www.physicsforums.com/blog.php?b=528</link>
			<pubDate>Fri, 21 Nov 2008 15:51:48 GMT</pubDate>
			<description><![CDATA[i've been doing some calculations, :blushing: 
 
and i've developed a theory that the bowliverse has not existed in its present form for ever, 
 
but has been expanding for about three years, 
 
and...]]></description>
			<content:encoded><![CDATA[<div>i've been doing some calculations, :blushing:<br />
<br />
and i've developed a theory that the bowliverse has not existed in its present form for ever,<br />
<br />
but has been expanding for about three years,<br />
<br />
and originally had a thinner and more flexible boundary. :smile:</div>

]]></content:encoded>
			<dc:creator>tiny-tim</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=528</guid>
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			<title>Panpsychism, explored</title>
			<link>http://www.physicsforums.com/blog.php?b=525</link>
			<pubDate>Thu, 20 Nov 2008 22:20:07 GMT</pubDate>
			<description><![CDATA[Reported at a local AAPT meeting on 11/10/07, googling "panpsychism" raised no hits in 1999, 700 in 2002, 40,000 in 2005, and 86,000 in 2007. With so much attention arising, I wonder whether any...]]></description>
			<content:encoded><![CDATA[<div>Reported at a local AAPT meeting on 11/10/07, googling &quot;panpsychism&quot; raised no hits in 1999, 700 in 2002, 40,000 in 2005, and 86,000 in 2007. With so much attention arising, I wonder whether any physicalist approach is(?) fruitful.  With life defined as a simple &quot;awareness&quot;, that is, between self and otherness, observed and observer, etc. it seems to imply the concept(s) of Heisenberg's principle.  Extending this idea, &quot;mass&quot; or &quot;energy&quot; at any level is &quot;aware&quot; of it's surroundngs. (i.e., any action must result in reaction to count, measure, or harmonize.). <br />
<br />
Biology has made progress in relating mass of living organisms over 21 orders of magnitude, from bacteria (less than a &quot;planck&quot; mass) to whales. (allometry). <br />
<br />
So, might one conclude that since light requires (needs?) mass to validate it's existence, mass requires (needs?) time to prove it's presence. In short, light makes mass and mass makes time.  Hmmmm.  <br />
<br />
Before I continue, comments welcome.</div>

]]></content:encoded>
			<dc:creator>SdogV</dc:creator>
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			<title>Translation</title>
			<link>http://www.physicsforums.com/blog.php?b=524</link>
			<pubDate>Thu, 20 Nov 2008 03:04:47 GMT</pubDate>
			<description>Please note that the blogs are not for asking for help or posting questions.  If you would like help, please feel free to post your question in the appropriate forum. 
 
Hootenanny</description>
			<content:encoded><![CDATA[<div>Please note that the blogs are not for asking for help or posting questions.  If you would like help, please feel free to post your question in the appropriate forum.<br />
<br />
Hootenanny</div>

]]></content:encoded>
			<dc:creator>toot997</dc:creator>
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		<item>
			<title>Counter a crackpot theory</title>
			<link>http://www.physicsforums.com/blog.php?b=523</link>
			<pubDate>Tue, 18 Nov 2008 22:18:52 GMT</pubDate>
			<description><![CDATA[A few years ago, when I was a kid, I had the idea that maybe mass creates mass. 
 
Here's how it came about,  
 
I knew that through high energy collisions, you can create mass out of relative energy...]]></description>
			<content:encoded><![CDATA[<div>A few years ago, when I was a kid, I had the idea that maybe mass creates mass.<br />
<br />
Here's how it came about, <br />
<br />
I knew that through high energy collisions, you can create mass out of relative energy between particles, when they collide at high enough speed, they can produce new particles.<br />
<br />
I also knew that the higher the temperature of any given body of mass, the faster particles are bouncing around, or the greater the kinetic energy between gas particles. <br />
<br />
I also knew that the core of the earth is extremely hot due to high pressures created though gravitational attraction. <br />
<br />
So I postulated that mass must be creating mass, because the center of the earth is really hot, and particles are colliding with eachother and creating more mass, thereby increasing the pressure. Creating a slow runaway effect.<br />
<br />
This runaway effect quickly dissuaded me, but then I thought this might be a slow process, and it continues until the body begins radiating the energy at a greater rate than it's creating energy.<br />
<br />
Then I saw Neil Adams &quot;Expanding Earth Theory&quot; on youtube, I found it intriguing and dissapointing. Intriguinging because it was the same idea I had, dissapointing because he made it seem like some crackpot theory.<br />
<br />
Although I doubt it describes reality, and that conservation of energy is wrong, I didn't see anything explicitly wrong with the idea. Is there something fundamental about the process of fusion I don't understand?</div>

]]></content:encoded>
			<dc:creator>WCOLtd</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=523</guid>
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		<item>
			<title>Hawking radiation for Kerr black holes</title>
			<link>http://www.physicsforums.com/blog.php?b=421</link>
			<pubDate>Mon, 17 Nov 2008 11:29:00 GMT</pubDate>
			<description><![CDATA[Temperature of a black hole (Hawking radiation)- 
 
<a href="javascript:;" onClick="latexPopup('tex', 'T=\\frac{\\kappa \\hbar}{2\\pi k_bc}')"><img src="latex_images/preview0-8.png" border=0...]]></description>
			<content:encoded><![CDATA[<div>Temperature of a black hole (Hawking radiation)-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'T=\\frac{\\kappa \\hbar}{2\\pi k_bc}')"><img src="latex_images/preview0-18.png" border=0 align=top alt='LaTeX Code: T=\\frac{\\kappa \\hbar}{2\\pi k_bc} '></a><br />
<br />
<br />
Killing surface gravity for a static black hole-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\kappa=\\frac{c^4}{4Gm}')"><img src="latex_images/preview0-19.png" border=0 align=top alt='LaTeX Code: \\kappa=\\frac{c^4}{4Gm} '></a><br />
<br />
<br />
Killing surface gravity for a rotating black hole-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\kappa=c^2\\ \\frac{(r_+-r_-)}{2\\left(r_+^2+a^2\\right)} =\\ 2\\left(1+\\frac{M}{\\sqrt{M^2-a^2}\\right)^{-1}}\\frac{c^4}{4Gm}')"><img src="latex_images/preview0-20.png" border=0 align=top alt='LaTeX Code: \\kappa=c^2\\ \\frac{(r_+-r_-)}{2\\left(r_+^2+a^2\\right)} =\\ 2\\left(1+\\frac{M}{\\sqrt{M^2-a^2}\\right)^{-1}}\\frac{c^4}{4Gm} '></a><br />
<br />
(while the second equation is good for a/M&lt;1 it doesn't work at exactly a/M=1 where the results should produce zero due to the outer and inner event horizons converging at the gravitational radius, leaving a naked singularity (as does the first equation). While the gradient of decrease is good up to a/M=1, zero at a/M=1 is implied. It does, however, work for a Schwarzschild solution at a=0).<br />
<br />
The second equation can be simplified to-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\kappa=2\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{-1}}\\frac{c^4}{4Gm}')"><img src="latex_images/preview0-21.png" border=0 align=top alt='LaTeX Code: \\kappa=2\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{-1}}\\frac{c^4}{4Gm} '></a><br />
<br />
where <i>a<sub>&#8727;</sub></i>=a/M<br />
<br />
<br />
A solution for Hawking radiation that applies to both static and rotating black holes is-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'T = 2\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{-1}} \\frac{\\hbar c^3}{8 \\pi G k_b m}')"><img src="latex_images/preview0-22.png" border=0 align=top alt='LaTeX Code: T = 2\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{-1}} \\frac{\\hbar c^3}{8 \\pi G k_b m} '></a><br />
<br />
<br />
Equations can be formulated for power (P) and time (t)-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'P=A\\epsilon \\sigma T^4')"><img src="latex_images/preview0-23.png" border=0 align=top alt='LaTeX Code: P=A\\epsilon \\sigma T^4 '></a><br />
<br />
where for a rotating black hole-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'A=8\\pi M\\left(M+\\sqrt{M^2-a^2}\\right)')"><img src="latex_images/preview0-24.png" border=0 align=top alt='LaTeX Code: A=8\\pi M\\left(M+\\sqrt{M^2-a^2}\\right) '></a><br />
<br />
which can be rewritten relative to the Schwarzschild equation as-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'A=\\frac{1}{2}\\left(1+\\sqrt{(1-a_\\ast^2)}\\right) \\frac{16 \\pi G^2m^2}{c^4}')"><img src="latex_images/preview0-25.png" border=0 align=top alt='LaTeX Code: A=\\frac{1}{2}\\left(1+\\sqrt{(1-a_\\ast^2)}\\right) \\frac{16 \\pi G^2m^2}{c^4} '></a><br />
<br />
Meaning the equations for power (P) and time (t) for a rotating black hole would be-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', 'P=\\frac{1}{2}\\left(1+\\sqrt{(1-a_\\ast^2)}\\right)\\frac{\\hbar c^6}{15360 \\pi G^2 m^2}\\ 16\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{-4}}')"><img src="latex_images/preview0-26.png" border=0 align=top alt='LaTeX Code: P=\\frac{1}{2}\\left(1+\\sqrt{(1-a_\\ast^2)}\\right)\\frac{\\hbar c^6}{15360 \\pi G^2 m^2}\\ 16\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{-4}} '></a> <br />
  <br />
<a href="javascript:;" onClick="latexPopup('tex', 't=2\\left(1+\\sqrt{(1-a_\\ast^2)}\\right)^{-1}\\ \\frac{5120 \\pi G^2 m^3}{\\hbar c^4}\\ \\frac{1}{16}\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{4}}')"><img src="latex_images/preview0-27.png" border=0 align=top alt='LaTeX Code: t=2\\left(1+\\sqrt{(1-a_\\ast^2)}\\right)^{-1}\\ \\frac{5120 \\pi G^2 m^3}{\\hbar c^4}\\ \\frac{1}{16}\\left(1+\\frac{1}{\\sqrt{(1-a_{\\ast}^2)}\\right)^{4}} '></a><br />
<br />
where <i>a<sub>&#8727;</sub></i>=a/M<br />
<br />
<br />
While the above is derived using current equations relating to Killing surface gravity, Hawking radiation and horizon surface area, it should be noted that some astrophysicists believe that a new definition of the vacuum within the ergoregion (between the ergosphere and the event horizon) should be defined in order to obtain both the thermal flux and the non-thermal emission from a Kerr black hole (see 'On the energy emission by a Kerr black hole in the superradiant range' by Anna Curir).<br />
<br />
<br />
'Black Hole Thermodynamics' by Narit Pidokrajt<br />
<a href="http://www.physto.se/~narit/bh.pdf" target="_blank">http://www.physto.se/~narit/bh.pdf</a><br />
page 10<br />
<br />
'Black Holes: An Introduction' by Derek J. Raine &amp; Edwin George Thomas<br />
<a href="http://books.google.com/books?id=oPTHJedi_uQC&amp;pg=PA59&amp;lpg=PR7&amp;ie=ISO-8859-1&amp;output=html" target="_blank">http://books.google.com/books?id=oPT...-1&amp;output=html</a> <br />
page 59<br />
<br />
static solutions-<br />
<a href="http://en.wikipedia.org/wiki/Hawking_radiation" target="_blank">http://en.wikipedia.org/wiki/Hawking_radiation</a></div>

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			<dc:creator>stevebd1</dc:creator>
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			<title>Kinetic theory of gases calculation</title>
			<link>http://www.physicsforums.com/blog.php?b=520</link>
			<pubDate>Sun, 16 Nov 2008 22:12:47 GMT</pubDate>
			<description>Homework is not allowed in blogs. 
 
Please post all homework type questions in the Homework Forum found here. 
 
http://physicsforums.com/forumdisplay.php?f=152</description>
			<content:encoded><![CDATA[<div>Homework is not allowed in blogs.<br />
<br />
Please post all homework type questions in the Homework Forum found here.<br />
<br />
<a href="http://physicsforums.com/forumdisplay.php?f=152" target="_blank">http://physicsforums.com/forumdisplay.php?f=152</a></div>

]]></content:encoded>
			<dc:creator>Amandasce</dc:creator>
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			<title>Smilies / emoticons</title>
			<link>http://www.physicsforums.com/blog.php?b=519</link>
			<pubDate>Sat, 15 Nov 2008 03:55:49 GMT</pubDate>
			<description><![CDATA[Image: http://www.myemoticons.com/emoticons/images/msn/smiley-says/thankyou.gif  
[ img]http://www.myemoticons.com/emoticons/images/msn/smiley-says/thankyou.gif[/img] 
 
Image:...]]></description>
			<content:encoded><![CDATA[<div><img src="http://www.myemoticons.com/emoticons/images/msn/smiley-says/thankyou.gif" border="0" alt="" /><br />
[ img]http://www.myemoticons.com/emoticons/images/msn/smiley-says/thankyou.gif[/img]<br />
<br />
<img src="http://www.myemoticons.com/emoticons/images/msn/smiley-says/thanx.gif" border="0" alt="" /><br />
[ img]http://www.myemoticons.com/emoticons/images/msn/smiley-says/thanx.gif[/img]<br />
<br />
<img src="http://www.myemoticons.com/emoticons/images/msn/smiley-says/ok.gif" border="0" alt="" /><br />
[ img]http://www.myemoticons.com/emoticons/images/msn/smiley-says/ok.gif[/img]<br />
<br />
<img src="http://www.myemoticons.com/emoticon-critic/funny/images/backflip.gif" border="0" alt="" /><br />
[ img]http://www.myemoticons.com/emoticon-critic/funny/images/backflip.gif[/img]<br />
<br />
<img src="http://www.myemoticons.com/emoticons/images/msn/moods/bounce.gif" border="0" alt="" /><br />
[ img]http://www.myemoticons.com/emoticons/images/msn/moods/bounce.gif[/img]<br />
<br />
<img src="http://www.myemoticons.com/emoticons/images/msn/moods/giggle.gif" border="0" alt="" /><br />
[ img]http://www.myemoticons.com/emoticons/images/msn/moods/giggle.gif[/img]<br />
<br />
<img src="http://www.websmileys.com/sm/fam/fam24.gif" border="0" alt="" /><br />
[ img]http://www.websmileys.com/sm/fam/fam24.gif[/img]<br />
<br />
<img src="http://www.websmileys.com/sm/drink/trink39.gif" border="0" alt="" /><br />
[ img]http://www.websmileys.com/sm/drink/trink39.gif[/img]</div>

]]></content:encoded>
			<dc:creator>Redbelly98</dc:creator>
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			<title>Killing field properties for black holes</title>
			<link>http://www.physicsforums.com/blog.php?b=514</link>
			<pubDate>Fri, 14 Nov 2008 20:34:52 GMT</pubDate>
			<description>_Killing vector field_  
 
_Azimuthal_   
A Killing vector field is a vector field on a differentiable manifold that preserves the metric over spacetime (from what I can gather, in very basic terms,...</description>
			<content:encoded><![CDATA[<div><u>Killing vector field</u> <br />
<br />
<u>Azimuthal</u>  <br />
A Killing vector field is a vector field on a differentiable manifold that preserves the metric over spacetime (from what I can gather, in very basic terms, a Killing vector field ensures smoothness of the metric, ranging from -1 (time-like) at infinity to zero (null) to 1 (space-like), if it exceeds 1 then the it normally increases to infinity). Although normally time-like (c^2 dt^2 &gt; dr^2), it does not need to be time-like everywhere outside the bh horizon. For Kerr metric, the azimuthal Killing vector field is- <br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\tag{1} \\kappa^2=g_{tt}=-\\frac{\\Delta-a^2sin^2\\theta}{\\rho^2}')"><img src="latex_images/preview0-38.png" border=0 align=top alt='LaTeX Code: \\tag{1} \\kappa^2=g_{tt}=-\\frac{\\Delta-a^2sin^2\\theta}{\\rho^2} '></a> <br />
<br />
where<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\Delta= r^{2}+a^{2}-2Mr')"><img src="latex_images/preview0-39.png" border=0 align=top alt='LaTeX Code: \\Delta= r^{2}+a^{2}-2Mr '></a><br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\rho^2=r^2+a^2 cos^2\\theta')"><img src="latex_images/preview0-40.png" border=0 align=top alt='LaTeX Code: \\rho^2=r^2+a^2 cos^2\\theta '></a><br />
<br />
and M=Gm/c^2 (gravitational radius) and a=J/mc (angular momentum per unit mass)<br />
<br />
which equals-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\kappa^2=-\\left(1-\\frac{2Mr}{r^{2}+a^{2}cos^{2}\\theta}\\right)')"><img src="latex_images/preview0-41.png" border=0 align=top alt='LaTeX Code: \\kappa^2=-\\left(1-\\frac{2Mr}{r^{2}+a^{2}cos^{2}\\theta}\\right) '></a><br />
<br />
Based on the equation above, divergence of the Killing field is at the event horizon for a static Schwarzschild bh and at the ergosphere for a rotating Kerr bh, co-ordinates become light-like (c^2 dt^2 = dr^2) at the point of divergence and then space-like beyond (c^2 dt^2 &lt; dr^2) (the results could be converted to velocity by assuming zero is the speed of light and -1 is zero velocity, <font face="Times New Roman"><font size="3"><i>&#954;</i></font></font>&gt;0 would imply v&gt;c which indicates space-like geodesics). The ergosphere equation is derived from the azimuthal Killing vector field-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\tag{2}r_{e\\pm}=M\\pm\\sqrt{M^2-a^2cos^2\\theta}')"><img src="latex_images/preview0-42.png" border=0 align=top alt='LaTeX Code: \\tag{2}r_{e\\pm}=M\\pm\\sqrt{M^2-a^2cos^2\\theta} '></a> <br />
<br />
Interestingly, an inner ergosphere r<sub>e-</sub> crops up within the boundary of the inner event horizon, implying that spacetime intervals in the azimuthal plane (but top and bottom of the singularity) become time-like again at some point within the inner event horizon.<br />
<br />
<u>Radial</u><br />
While the above could be described as an azimuthal Killing vector field that recognises the ergosphere, there should also be a 'radial' Killing vector field that recognises the event horizons. This would increase from -1 at infinity to 0 at the outer event horizon (r<sub>+</sub>) where it would change sign (i.e. become space-like), peak at the gravitational radius (M) then drop back to 0 at the inner event horizon (r<sub>-</sub>) where it would become time-like again, increasing to 1(?) towards r=0. (&#916;=r^2+a^2-2Mr could be described as a kind of radial Killing vector field as it decreases from infinity to zero at the outer event horizon, changing sign in the shallow region of the bh, peaking at M, dropping back to zero at the inner event horizon and reversing sign again in the deep region of the bh. The radii for the outer and inner event horizon are derived from &#916;, it also helps to define time-like &amp; space-like geodesics).<br />
<br />
A radial Killing vector field using &#916; might look something like-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\kappa^2=-\\left(\\frac{r^2+a^2-2Mr}{r^2+a^2}\\right)=-\\left(1-\\frac{2Mr}{r^{2}+a^2}\\right)')"><img src="latex_images/preview0-43.png" border=0 align=top alt='LaTeX Code: \\kappa^2=-\\left(\\frac{r^2+a^2-2Mr}{r^2+a^2}\\right)=-\\left(1-\\frac{2Mr}{r^{2}+a^2}\\right) '></a><br />
<br />
which reduces the quantities of &#916; to range between -1, 0 and 1 (-1, 0 and &#8734; for the Schwarzschild solution). The equations that denote the outer and inner event horizons would be derived from this equation (see equation 5).<br />
<br />
<br />
<u>Killing Surface Gravity</u><br />
<br />
For a static Schwarzschild black hole-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\tag{3}\\kappa=\\frac{c^4}{4GM}')"><img src="latex_images/preview0-44.png" border=0 align=top alt='LaTeX Code: \\tag{3}\\kappa=\\frac{c^4}{4GM} '></a> <br />
<br />
For a rotating Kerr black hole-<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\tag{4}\\kappa_{\\pm}=c^2\\ \\frac{r_{\\pm}-r_{\\mp}}{2\\left(r_{\\pm}^2+a^2\\right)}')"><img src="latex_images/preview0-45.png" border=0 align=top alt='LaTeX Code: \\tag{4}\\kappa_{\\pm}=c^2\\ \\frac{r_{\\pm}-r_{\\mp}}{2\\left(r_{\\pm}^2+a^2\\right)} '></a><br />
<br />
where<br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\tag{5} r_\\pm=M\\pm\\sqrt{M^2-a^2}')"><img src="latex_images/preview0-46.png" border=0 align=top alt='LaTeX Code: \\tag{5} r_\\pm=M\\pm\\sqrt{M^2-a^2} '></a><br />
<br />
r<sub>+</sub> is the outer event horizon, r<sub>-</sub> is the inner event horizon, M is the gravitational constant (M=Gm/c^2) and <i>a</i> is the spin parameter in metres (<i>a</i>=J/mc)<br />
<br />
Surface gravity of inner and outer horizons for a rotating 3 sol mass black hole with a spin parameter of 0.95 are-<br />
<br />
<font face="Times New Roman"><font size="3"><i>&#954;</i></font></font><sub>+</sub>=2.4136e12 m/s^2<br />
<br />
<font face="Times New Roman"><font size="3"><i>&#954;</i></font></font><sub>-</sub>=-4.6053e12 m/s^2<br />
<br />
which is interesting as it implies that gravity is negative at the inner event horizon.<br />
<br />
<br />
<u>Killing Horizon</u><br />
<br />
<a href="javascript:;" onClick="latexPopup('tex', '\\tag{6}\\Omega_H=c\\ \\frac{a}{\\left(r_{\\pm}^2+a^2\\right)}=c\\ \\frac{1}{2} \\frac{a}{M} \\frac{1}{r_{\\pm}}')"><img src="latex_images/preview0-47.png" border=0 align=top alt='LaTeX Code: \\tag{6}\\Omega_H=c\\ \\frac{a}{\\left(r_{\\pm}^2+a^2\\right)}=c\\ \\frac{1}{2} \\frac{a}{M} \\frac{1}{r_{\\pm}} '></a><br />
<br />
Frame dragging rates of inner and outer horizon (as measured from infinity) for a 3 sol mass black hole with a spin parameter of 0.95-<br />
<br />
<font face="Times New Roman">&#937;</font><sub>+</sub> = 24,492.744 rads/second <br />
<br />
<font face="Times New Roman">&#937;</font><sub>-</sub> = 46,734.646 rads/second<br />
<br />
<br />
Both the Killing surface gravity and Killing horizon are taken where the Killing vector field becomes null (i.e. where <font face="Times New Roman"><font size="3"><i>&#954;</i></font></font>=0) though I'm not entirely sure how this applies to the ergosphere. If Killing surface gravity becomes zero at the Killing horizon then the horizon is considered degenerate, this normally occurs when a=M, i.e. maximum spin. <br />
<br />
<br />
<br />
(1)- page 256, (4)(5)(6)- page 253<br />
'Compact Objects in Astrophysics' by Max Camenzind <br />
<a href="http://www.lsw.uni-heidelberg.de/users/mcamenzi/CObjects_06.pdf" target="_blank">http://www.lsw.uni-heidelberg.de/use...Objects_06.pdf</a><br />
<br />
(2)- page 11<br />
'Black Holes: Structure, Formation and Practical Applications' by Klaas Hartmann<br />
<a href="http://www.klaashartmann.com/papers/UG_BlackHoleEssay.pdf" target="_blank">http://www.klaashartmann.com/papers/...kHoleEssay.pdf</a><br />
<br />
(3)-<br />
<a href="http://en.wikipedia.org/wiki/Surface_gravity" target="_blank">http://en.wikipedia.org/wiki/Surface_gravity</a></div>


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			<dc:creator>stevebd1</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=514</guid>
		</item>
		<item>
			<title>How do I visualize particles?</title>
			<link>http://www.physicsforums.com/blog.php?b=513</link>
			<pubDate>Wed, 12 Nov 2008 19:24:44 GMT</pubDate>
			<description>How do I visualize particles? 
If you have been reading my blog then you have a pretty good idea. 
	*Perfect Symmetry vs. broken symmetry (CPT)* 
 
1.	First I realize that what we “see” is an...</description>
			<content:encoded><![CDATA[<div>How do I visualize particles?<br />
If you have been reading my blog then you have a pretty good idea.<br />
	<b>Perfect Symmetry vs. broken symmetry (CPT)</b><br />
<br />
1.	First I realize that what we “see” is an <i>interpretation</i> of what is achieved by experiments<br />
2.	Experiments can only “see” a <i>confined</i> proton, neutron, size of approx. 10^-15. The interpretations are the QED of the Standard model .<br />
3.	At a smaller scale, QCD, inside the proton, <b>models are still being developed</b>, and tested against the results of experiments. If a physical minimum length, (ie. planck scale), is applied as a condition, then LQG, Lattice QCD etc. which all use a minimum length, would be a more accurate description and you can only get to a 4-Manifold, A3 lattice, a cube.  <br />
4.	Experiments at high pressure and density have produced a liquid of quark gluon, which is not confined, which can be modeled as a perfect liquid and maybe as perfect symmetry.<br />
<br />
For high school students, read my blog and see if there is anything there that you want to use.<br />
======<br />
<a href="http://en.wikipedia.org/wiki/Gauge_theory" target="_blank">http://en.wikipedia.org/wiki/Gauge_theory</a> <br />
========= <br />
Read what John Baez has been presenting and see if what I have been saying “rings a bell”. <br />
John Baez, at n-category café has started seminars/lessons on Lie Theory.<br />
<a href="http://golem.ph.utexas.edu/category/2008/09/lie_theory_through_examples_1.html#more" target="_blank">http://golem.ph.utexas.edu/category/...es_1.html#more</a> <br />
Lie Theory Through Examples 1<br />
Posted by John Baez<br />
<br />
<a href="http://golem.ph.utexas.edu/category/2008/10/lie_theory_through_examples_2.html#more" target="_blank">http://golem.ph.utexas.edu/category/...es_2.html#more</a> <br />
Lie Theory Through Examples 2<br />
Posted by John Baez<br />
======== <br />
Question:<br />
Could you give your definition of dimension and minimum length as it used for this subject.<br />
Answer:<br />
I’m using the usual definitions of ‘dimension’ and ‘length’ that apply to n-dimensional Euclidean space.<br />
------ <br />
Note: That means he is not using minimum length, or Planck length.<br />
------ <br />
<a href="http://en.wikipedia.org/wiki/Distance" target="_blank">http://en.wikipedia.org/wiki/Distance</a> <br />
Distance is a numerical description of how far apart objects are<br />
<a href="http://en.wikipedia.org/wiki/Metric_(mathematics" target="_blank">http://en.wikipedia.org/wiki/Metric_(mathematics</a>) <br />
In mathematics, a metric or distance function is a function which defines a distance between elements of a set.<br />
<a href="http://en.wikipedia.org/wiki/Dimension" target="_blank">http://en.wikipedia.org/wiki/Dimension</a> <br />
dimension<br />
<a href="http://en.wikipedia.org/wiki/Euclidean_space" target="_blank">http://en.wikipedia.org/wiki/Euclidean_space</a> <br />
n-dimensional Euclidean space <br />
======= <br />
Note: If you accept that particles are point like then you can get to E8.<br />
If a physical minimum length, (planck scale), is applied as a condition, then LQG, Lattice QCD etc. which all use a minimum length, would be a more accurate description and you can only get to a 4-Manifold, A3 lattice, a cube.  <br />
========= <br />
===== <br />
<a href="http://math.ucr.edu/home/baez/qg-fall2008/lie3.pdf" target="_blank">http://math.ucr.edu/home/baez/qg-fall2008/lie3.pdf</a>   <br />
Lie Theory Through Examples 3<br />
========<br />
<a href="http://golem.ph.utexas.edu/category/2008/10/lie_theory_through_examples_4.html#more" target="_blank">http://golem.ph.utexas.edu/category/...es_4.html#more</a> <br />
Lie Theory Through Examples 4<br />
======== <br />
The A3 lattice concept ....<br />
12  points on those 12 edges of the cube.<br />
By using the concept of minimum length and the definition of a dimension, you can squeeze 4 dimensions with a length of 4 into the same space occupied by 3 dimension.<br />
Then using the concept of a vibrating string you obtain the concept of 12 energy nodes on those edges which produces the cubic lattice and perfect symmetry. Look at the attached picture. <br />
<img src="http://www.geocities.com/j_jall/synchronization-2.gif" border="0" alt="" /><br />
I assume that before too long, John Baez’s lectures will show if there are errors in my assumptions/thinking that need corrections. <br />
 <br />
======== <br />
<br />
Here another interesting image to go with John Baez’ image<br />
<img src="http://www.fnal.gov/pub/presspass/images/bbaryon_jphalf_spect_Omb-m.jpg" border="0" alt="" />  <br />
from FERMILAB <br />
<a href="http://www.fnal.gov/pub/presspass/press_releases/Dzero_Omega-sub-b.html" target="_blank">http://www.fnal.gov/pub/presspass/pr...ega-sub-b.html</a> <br />
Fermilab physicists discover &quot;doubly strange&quot; particle <br />
========= <br />
Another blog reference <br />
<a href="http://www.math.columbia.edu/~woit/wordpress/" target="_blank">http://www.math.columbia.edu/~woit/wordpress/</a> <br />
Not Even Wrong<br />
 Notes on BRST I: Representation Theory and Quantum Mechanics<br />
November 5th, 2008<br />
<br />
======= <br />
~~~ Since I am learning, I reserve the right to change my mind. ~~~~<br />
======</div>

]]></content:encoded>
			<dc:creator>jal</dc:creator>
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		<item>
			<title>Not Much Going On</title>
			<link>http://www.physicsforums.com/blog.php?b=506</link>
			<pubDate>Sun, 09 Nov 2008 01:36:48 GMT</pubDate>
			<description>Well my daughter is off camping this weekend with her friends and my son is off to a cheerleading competition with friend-girls.  My son is so busy on weekends.  He is 16 and has a busy social life. ...</description>
			<content:encoded><![CDATA[<div>Well my daughter is off camping this weekend with her friends and my son is off to a cheerleading competition with friend-girls.  My son is so busy on weekends.  He is 16 and has a busy social life.  He doesn't get his chores done even though he has little to do.  My kids are spoiled.  I've always bought them anything they wanted.  But now that has to change.  My husband is now going into the homeowner business since new housing is in the toilet.  He has a job down the street....it is a screened-in porch over an existing deck.  He already has had someone stop to say after he is done there to go to his house.  So hopefully referrals will get us through winter. I still need to put out flyers.  As for me I am wasting away.  I sleep most of the day even though I don't think it is quality sleep.  I just lay there talking in my head and having strange dreams.  I do what I have to do, but I am depressed.  Maybe because I drink beer.  Oh well.  No need to talk about that..I'm sure you all are sick of me talking about drinking.  Gotta go, Leah</div>

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			<dc:creator>Leah</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=506</guid>
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		<item>
			<title>… inflationary bowliverse … ?</title>
			<link>http://www.physicsforums.com/blog.php?b=504</link>
			<pubDate>Sat, 08 Nov 2008 11:15:45 GMT</pubDate>
			<description>did i lose weight during the big move :blushing:, 
or did the bowliverse suddenly expand? :confused:</description>
			<content:encoded><![CDATA[<div>did i lose weight during the <i>big move</i> :blushing:,<br />
<blockquote>or did the bowliverse suddenly expand? :confused:</blockquote></div>

]]></content:encoded>
			<dc:creator>tiny-tim</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=504</guid>
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			<title>brain teasers</title>
			<link>http://www.physicsforums.com/blog.php?b=493</link>
			<pubDate>Mon, 03 Nov 2008 00:38:06 GMT</pubDate>
			<description><![CDATA[a homeless man can collect cigar butts-5 can make 1 cigar. he collects 100 cigar butts. how many cigars can he make? 
 
 
 
ill let u guys work it out =[] 
 
 
1  2  3  4  5  6  7  8  9=100 
 
add...]]></description>
			<content:encoded><![CDATA[<div>a homeless man can collect cigar butts-5 can make 1 cigar. he collects 100 cigar butts. how many cigars can he make?<br />
<br />
<br />
<br />
ill let u guys work it out =[]<br />
<br />
<br />
1  2  3  4  5  6  7  8  9=100<br />
<br />
add one addition sign and two subtraction signs to the above equation to make it true,but<br />
it must stay in the same order, but you can move the addition and subtractions signs to any order:uhh:<br />
<br />
<br />
<br />
u guys can take this one =[]<br />
<br />
<br />
<br />
you have to balance 16oz of water with 16oz of weights... you have an unlimited spiggot but u only have 1 chance to  do it... make it exact, you only get a 5 oz cup and a 7 oz cup, the cups weigh the same, and the bowls weigh the same&lt;this is all oz weight, not fl oz&gt;<br />
<br />
u guys want an answer?</div>

]]></content:encoded>
			<dc:creator>alexk174</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=493</guid>
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		<item>
			<title>… halloween … BOO! …</title>
			<link>http://www.physicsforums.com/blog.php?b=491</link>
			<pubDate>Fri, 31 Oct 2008 13:22:09 GMT</pubDate>
			<description>boo! :biggrin: 
 
this is my halloween costume (http://www.bbc.co.uk/southerncounties/community/customer_care/colin_halloween_270.jpg) :smile:</description>
			<content:encoded><![CDATA[<div>boo! :biggrin:<br />
<br />
<div align="center">this is my <a href="http://www.bbc.co.uk/southerncounties/community/customer_care/colin_halloween_270.jpg" target="_blank">halloween costume</a> :smile:</div></div>

]]></content:encoded>
			<dc:creator>tiny-tim</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=491</guid>
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		<item>
			<title>The Dow, 2008 vs. 1987 vs. 1929   (as of 21 Nov. 2008)</title>
			<link>http://www.physicsforums.com/blog.php?b=488</link>
			<pubDate>Wed, 29 Oct 2008 21:10:30 GMT</pubDate>
			<description>A comparison of the Dow Jones Industrial Average during the financial crashes of 1929, 1987, and 2008. 
 
Image:...</description>
			<content:encoded><![CDATA[<div>A comparison of the Dow Jones Industrial Average during the financial crashes of 1929, 1987, and 2008.<br />
<br />
<img src="http://i49.photobucket.com/albums/f282/redbelly98/PhysicsForums/TheDow2008-1987-1929_2008-11-21.gif?t=1227309678" border="0" alt="" /><br />
<br />
Here is a five-year graph:<br />
<br />
<img src="http://i49.photobucket.com/albums/f282/redbelly98/PhysicsForums/TheDow2008-1987-1929_5yr_2008-11-21.gif?t=1227309680" border="0" alt="" /><br />
<br />
The Dow took quite a different track in the years following <b><font color="YellowGreen">1987 (green curve)</font></b> than it did following <font color="Red"><b>1929 (red curve)</b></font>.  However, it was<b> not until May</b> following either of these crashes that there was a noticeable trend toward either recovery (1988) or further declines (1930).<br />
<br />
The lowest close of The Dow during the Great Depression was on 8 July 1932, when it closed at 41.22.  This would be the equivalent of about <b>1330 points today</b>.<br />
<br />
<font size="2">I will try to update this graph weekly, or as time permits.</font></div>

]]></content:encoded>
			<dc:creator>Redbelly98</dc:creator>
			<guid isPermaLink="true">http://www.physicsforums.com/blog.php?b=488</guid>
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