web1110
Jul19-04, 04:09 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOK, it is asserted that a black hole may rotate. I saw the preceeding\nquestion and it didn\'t help me with my question/\n\nAt the event horizon, the movement of time comes to a halt for all practical\npurposes, yet an equation of a rotating object is described with an \'omega\nt\' exponent. In this case, \'omege t\' is a constant. Rotation is zero.\n\nIf time does not advance, how can something rotate?\n\nBill\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>OK, it is asserted that a black hole may rotate. I saw the preceeding
question and it didn't help me with my question/
At the event horizon, the movement of time comes to a halt for all practical
purposes, yet an equation of a rotating object is described with an '\omega
t' exponent. In this case, 'omege t' is a constant. Rotation is zero.
If time does not advance, how can something rotate?
Bill
tessel@tum.bot
Jul20-04, 04:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 19 Jul 2004, web1110 wrote:\n\n> OK, it is asserted that a black hole may rotate. I saw the preceeding\n^^^^^^^^^^^^^^\n> question and it didn\'t help me with my question/\n^^^^^^^^ ^^^^^^^^^^^\nreply?\n\nI don\'t know what question(s?) you mean, since you didn\'t quote any text\nand you didn\'t include a "Reference" line in the header of your post.\n(Perhaps you clicked on the "post" button rather than the "reply" button\non your web browser?)\n\nHowever, I seem to remember that I recently replied to a question\nconcerning black hole rotation. I can\'t recall details, but I often reply\nto questions at a rather high level of sophistication--- if so, I may well\nhave unintentionally confused you! If a poster specifically states that\nhe/she is a high school student or whatever, I will sometimes try to reply\nat an appropriate level (John Baez was much better at this than I am,\nhowever), and if not I will at least warn readers that my reply is aimed\nat the "default level" of this newsgroup (which I like to think of as\n"first or second year graduate student in math/physics").\n\n> At the event horizon, the movement of time comes to a halt for all practical\n> purposes,\n\nI know why you say that, but this is a VCM (very common misconception).\nIn fact, gtr does not say anything of the sort!\n\nHere is a website which offers help at various levels (popular to research\nlevel):\n\nhttp://math.ucr.edu/home/baez/relativity.html\n\nI suggest you look there for the sci.physics.relativity FAQ.\n\n> yet an equation of a rotating object is described with an \'omega t\'\n> exponent. In this case, \'omege t\' is a constant. Rotation is zero.\n^^^^^^^^\n???\n\nAre you thinking of "angular velocity" omega? (Multiplying by time t will\ngive net rotation since time zero, for an object which is rotating with\nconstant angular velocity.) Maybe even the Euler equation for a spinning\nobject in -Newtonian mechanics-? If so, one problem here is that the\nEuler equation for a spinning object isn\'t a relativistic equation.\n\nThe concept of "rigidly rotating objects" turns out to be, strictly\nspeaking, -inadmissible- even in str. And the notion of "rotating\nobjects" in gtr is even trickier! (Be aware that if you mention "black\nholes" without specifying a theory of gravity, be aware that readers are\nlikely to assume that you mean the current "default theory", gtr).\nNonetheless, with sufficient care, one -can- treat rotating objects in\ngtr, of course, including black holes (e.g. the famous Kerr vacuum\nsolution), and--- again, with sufficient care--- one can make sense of\n"angular velocity" of at least "an isolated body in an asymptotically flat\nspacetime". Fortunately, "Kerr objects" qualify as such. (Be aware that\nif you mention "rotating black hole" without further qualification, most\nreaders are likely to assume that you mean a Kerr hole, even though the\nEFE admits a huge variety of solutions modeling rotating black holes.)\n\nWhat I just said probably won\'t make sense yet, but for further reference\nnote that the FAQ pages I just mentioned discuss these issues (sketchily).\n\n> If time does not advance, how can something rotate?\n\nVery very -very- roughly speaking: fear not, Kerr holes do have a well\ndefined mass and angular momentum (although justifying this takes\nnontrivial sophistication/effort), but no observer in a Kerr vacuum ever\nexperiences anything like "time slowing" (that wouldn\'t even make\nsense!)--- not even if he happens to fall through the horizon--- but if he\nis inside the "ergosphere" (you can think of this as a surface just\noutside the horizon), then he must rotate along with the hole. (A\nrelevant buzzword here is "frame dragging".) Another very basic point\n(but notoriously hard to grasp for beginners) is that the event horizon is\na "global" concept, but gravitational field ("tidal force field") is a\nlocal one; this means that an observer falling through the horizon won\'t\nnotice anything special. Indeed, in principle, we could be inside the\nhorizon of a black hole right now, but not yet know it! (Buzzword:\n"Vaidya thought experiments".)\n\nRight now this probably won\'t make much sense to you. As a first step\ntoward basic intuition for black holes, I think you need to back up and\nstudy the geometrical model (Minkowski spacetime) for relativistic\nkinematics (aka "str") versus Galilean kinematics. A very good book for\nthis (which should be accessible to college and even high school students\nwith only modest mathematical background) is:\n\nauthor = {Edwin F. Taylor and John Archibald Wheeler},\ntitle = {Spacetime Physics: Introduction to Special Relativity},\nedition = {Second},\npublisher = {W. H. Freeman},\nyear = 1992}\n\nNext, you can study a semitechnical book introducing the geometry of black\nholes. One I like very much, which is written at a similar level to\nTaylor & Wheeler, is:\n\nauthor = {Geroch, Robert},\ntitle = {General relativity from {A} to {B}},\npublisher = {University of Chicago Press},\nyear = 1978}\n\n(recently reprinted); a more comprehensive book which would be a good\nsecond book is\n\nauthor = {Robert M. Wald},\ntitle = {Space, time, and gravity: the theory of the big bang and black\nholes},\npublisher = {University of Chicago Press},\nyear = 1992}\n\nAt the same time, you can study the FAQ cited above.\n\nIf you follow my advice, I think you will find that you can achieve a good\ngeometrical intuition for nonrotating holes from Geroch\'s book, and a less\naccurate but still valuable intuition for rotating holes from Wald\'s book,\neven if you have only a very modest mathematical background. You will\nhowever need a good geometric imagination.\n\nFor the definitions of mass and angular momentum of "isolated bodies in\nasymptotically flat spacetimes", you\'ll need to study gtr at the advanced\nundergraduate level. A good textbook for this (and much more) is:\n\nauthor = {Sean Carroll},\ntitle = {Spacetime and geometry: an introduction to general relativity},\npublisher = {Addison-Wesley},\nyear = 2004}\n\nA slightly more advanced book which is also excellent on this topic is\n\nauthor = {Hans Stephani},\ntitle = {General Relativity: An Introduction of the Theory of the\nGravitational Field},\npublisher = {Cambridge University Press},\nedition = {Second},\nnote = {translated by {J}ohn {S}tewart and {M}artin {P}ollock},\nyear = 1990}\n\n"T. Essel" (hiding somewhere in cyberspace)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 19 Jul 2004, web1110 wrote:
> OK, it is asserted that a black hole may rotate. I saw the preceeding
^^^^^^^^^^^^^^
> question and it didn't help me with my question/
^^^^^^^^ ^^^^^^^^^^^
reply?
I don't know what question(s?) you mean, since you didn't quote any text
and you didn't include a "Reference" line in the header of your post.
(Perhaps you clicked on the "post" button rather than the "reply" button
on your web browser?)
However, I seem to remember that I recently replied to a question
concerning black hole rotation. I can't recall details, but I often reply
to questions at a rather high level of sophistication--- if so, I may well
have unintentionally confused you! If a poster specifically states that
he/she is a high school student or whatever, I will sometimes try to reply
at an appropriate level (John Baez was much better at this than I am,
however), and if not I will at least warn readers that my reply is aimed
at the "default level" of this newsgroup (which I like to think of as
"first or second year graduate student in math/physics").
> At the event horizon, the movement of time comes to a halt for all practical
> purposes,
I know why you say that, but this is a VCM (very common misconception).
In fact, gtr does not say anything of the sort!
Here is a website which offers help at various levels (popular to research
level):
http://math.ucr.edu/home/baez/relativity.html
I suggest you look there for the sci.physics.relativity FAQ.
> yet an equation of a rotating object is described with an '\omega t'
> exponent. In this case, 'omege t' is a constant. Rotation is zero.
^^^^^^^^
???
Are you thinking of "angular velocity" \omega? (Multiplying by time t will
give net rotation since time zero, for an object which is rotating with
constant angular velocity.) Maybe even the Euler equation for a spinning
object in -Newtonian mechanics-? If so, one problem here is that the
Euler equation for a spinning object isn't a relativistic equation.
The concept of "rigidly rotating objects" turns out to be, strictly
speaking, -inadmissible- even in str. And the notion of "rotating
objects" in gtr is even trickier! (Be aware that if you mention "black
holes" without specifying a theory of gravity, be aware that readers are
likely to assume that you mean the current "default theory", gtr).
Nonetheless, with sufficient care, one -can- treat rotating objects in
gtr, of course, including black holes (e.g. the famous Kerr vacuum
solution), and--- again, with sufficient care--- one can make sense of
"angular velocity" of at least "an isolated body in an asymptotically flat
spacetime". Fortunately, "Kerr objects" qualify as such. (Be aware that
if you mention "rotating black hole" without further qualification, most
readers are likely to assume that you mean a Kerr hole, even though the
EFE admits a huge variety of solutions modeling rotating black holes.)
What I just said probably won't make sense yet, but for further reference
note that the FAQ pages I just mentioned discuss these issues (sketchily).
> If time does not advance, how can something rotate?
Very very -very- roughly speaking: fear not, Kerr holes do have a well
defined mass and angular momentum (although justifying this takes
nontrivial sophistication/effort), but no observer in a Kerr vacuum ever
experiences anything like "time slowing" (that wouldn't even make
sense!)--- not even if he happens to fall through the horizon--- but if he
is inside the "ergosphere" (you can think of this as a surface just
outside the horizon), then he must rotate along with the hole. (A
relevant buzzword here is "frame dragging".) Another very basic point
(but notoriously hard to grasp for beginners) is that the event horizon is
a "global" concept, but gravitational field ("tidal force field") is a
local one; this means that an observer falling through the horizon won't
notice anything special. Indeed, in principle, we could be inside the
horizon of a black hole right now, but not yet know it! (Buzzword:
"Vaidya thought experiments".)
Right now this probably won't make much sense to you. As a first step
toward basic intuition for black holes, I think you need to back up and
study the geometrical model (Minkowski spacetime) for relativistic
kinematics (aka "str") versus Galilean kinematics. A very good book for
this (which should be accessible to college and even high school students
with only modest mathematical background) is:
author = {Edwin F. Taylor and John Archibald Wheeler},
title = {Spacetime Physics: Introduction to Special Relativity},
edition = {Second},
publisher = {W. H. Freeman},
year = 1992}
Next, you can study a semitechnical book introducing the geometry of black
holes. One I like very much, which is written at a similar level to
Taylor & Wheeler, is:
author = {Geroch, Robert},
title = {General relativity from {A} to {B}},
publisher = {University of Chicago Press},
year = 1978}
(recently reprinted); a more comprehensive book which would be a good
second book is
author = {Robert M. Wald},
title = {Space, time, and gravity: the theory of the big bang and black
holes},
publisher = {University of Chicago Press},
year = 1992}
At the same time, you can study the FAQ cited above.
If you follow my advice, I think you will find that you can achieve a good
geometrical intuition for nonrotating holes from Geroch's book, and a less
accurate but still valuable intuition for rotating holes from Wald's book,
even if you have only a very modest mathematical background. You will
however need a good geometric imagination.
For the definitions of mass and angular momentum of "isolated bodies in
asymptotically flat spacetimes", you'll need to study gtr at the advanced
undergraduate level. A good textbook for this (and much more) is:
author = {Sean Carroll},
title = {Spacetime and geometry: an introduction to general relativity},
publisher = {Addison-Wesley},
year = 2004}
A slightly more advanced book which is also excellent on this topic is
author = {Hans Stephani},
title = {General Relativity: An Introduction of the Theory of the
Gravitational Field},
publisher = {Cambridge University Press},
edition = {Second},
note = {translated by {J}ohn {S}tewart and {M}artin {P}ollock},
year = 1990}
"T. Essel" (hiding somewhere in cyberspace)
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n"web1110" <web02@comcast.net> wrote in message news:<AfqdnXOqy_n4KmfdRVn-hA@comcast.com>...\n> OK, it is asserted that a black hole may rotate. I saw the preceeding\n> question and it didn\'t help me with my question/\n>\n> At the event horizon, the movement of time comes to a halt for all practical\n> purposes, yet an equation of a rotating object is described with an \'omega\n> t\' exponent. In this case, \'omege t\' is a constant. Rotation is zero.\n>\n> If time does not advance, how can something rotate?\n>\n> Bill\n\nFrom the point of view of a distant observer, an object would appear\nto take an infinite time to fall into a black hole. From the point of\nview of the person falling into the black hole, they would take a\nshort finite time to fall in.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"web1110" <web02@comcast.net> wrote in message news:<AfqdnXOqy_n4KmfdRVn-hA@comcast.com>...
> OK, it is asserted that a black hole may rotate. I saw the preceeding
> question and it didn't help me with my question/
>
> At the event horizon, the movement of time comes to a halt for all practical
> purposes, yet an equation of a rotating object is described with an '\omega
> t' exponent. In this case, 'omege t' is a constant. Rotation is zero.
>
> If time does not advance, how can something rotate?
>
> Bill
From the point of view of a distant observer, an object would appear
to take an infinite time to fall into a black hole. From the point of
view of the person falling into the black hole, they would take a
short finite time to fall in.
Michael Varney
Jul21-04, 05:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Ulmo" <ulmo@cheerful.com> wrote in message\nnews:53ca460a.0407200927.157437af@posting.google.com...\n>\n>\n>\n> "web1110" <web02@comcast.net> wrote in message\nnews:<AfqdnXOqy_n4KmfdRVn-hA@comcast.com>...\n> > OK, it is asserted that a black hole may rotate. I saw the preceeding\n> > question and it didn\'t help me with my question/\n> >\n> > At the event horizon, the movement of time comes to a halt for all\npractical\n> > purposes, yet an equation of a rotating object is described with an\n\'omega\n> > t\' exponent. In this case, \'omege t\' is a constant. Rotation is zero.\n> >\n> > If time does not advance, how can something rotate?\n> >\n> > Bill\n>\n> From the point of view of a distant observer, an object would appear\n> to take an infinite time to fall into a black hole.\n\nExcept that in reality, the image of the object would completely disappear\nafter a short and finite time for a distant observer.\n\n> From the point of\n> view of the person falling into the black hole, they would take a\n> short finite time to fall in.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Ulmo" <ulmo@cheerful.com> wrote in message
news:53ca460a.0407200927.157437af@posting.google.com...
>
>
>
> "web1110" <web02@comcast.net> wrote in message
news:<AfqdnXOqy_n4KmfdRVn-hA@comcast.com>...
> > OK, it is asserted that a black hole may rotate. I saw the preceeding
> > question and it didn't help me with my question/
> >
> > At the event horizon, the movement of time comes to a halt for all
practical
> > purposes, yet an equation of a rotating object is described with an
'\omega
> > t' exponent. In this case, 'omege t' is a constant. Rotation is zero.
> >
> > If time does not advance, how can something rotate?
> >
> > Bill
>
> From the point of view of a distant observer, an object would appear
> to take an infinite time to fall into a black hole.
Except that in reality, the image of the object would completely disappear
after a short and finite time for a distant observer.
> From the point of
> view of the person falling into the black hole, they would take a
> short finite time to fall in.
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