Re: Black holes and Barbero-Immirzi [Archive]

John Baez

May19-04, 03:39 AM

carlip@no-physics-spam.ucdavis.edu

May25-04, 01:33 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>John Baez <baez@galaxy.ucr.edu> wrote:\n\n> But the real problem with this Hod-Dreyer idea of relating quasinormal\n> modes to black hole entropy is not the SU(2) versus SO(3) business.\n> It\'s that the idea doesn\'t seem to work for *rotating* black holes:\n\n> Lubos Motl, Andrew Neitzke\n> Asymptotic black hole quasinormal frequencies\n> http://www.arXiv.org/abs/hep-th/0301173\n\nTo add to the confusion, though: the basic ``correspondence principle,\'\'\nas proposed by Bekenstein, *does* work for rotating (2+1)-dimensional\n(BTZ) black holes. In fact, it works remarkably well -- it reproduces\nnot only parts of the basic structure of the asymptotic Virasoro algebra,\nbut also a piece of an underlying substructure that\'s been proposed as\na quantization of the boundary Liouville theory. See Birmingham, Carlip,\nand Chen, hep-th/0305113, Class. Quant. Grav. 20 (2003) L239. But if\nyou look at the details of the correspondence, they look very different\nfrom the Hod-Dreyer version.\n\nTo add even further to the confusion: a modified version of Bekenstein\'s\n``correspondence principle\'\' also holds for several large classes of\nnear-extremal charged, rotating black holes of the sort that are fairly\nwell understood in string theory. These black holes have a near-horizon\ngeometry that looks like (BTZ)xS^n, and if you apply the correspondence\nprinciple to the corresponding BTZ quasinormal frequencies, you get quite\na bit of correct information about the string theory description -- not\njust the right quantization of energy and momentum flowing around the\nblack string, but even the right ``charge fractionization\'\' that\'s\nusually explained in terms of branes wrapping around cycles more than\nonce. See Birmingham and Carlip, hep-th/0311090, Phys. Rev. Lett. 92\n(2004) 111302. Again, though, the details look very different from the\nHod-Dreyer results. In fact, the relevant modes aren\'t even ordinary\nquasinormal modes any more (they\'re quasinormal-like modes for the near-\nhorizon geometry, but require different boundary conditions at infinity).\nWe don\'t yet understand what they are, though they appear to be related\nto thermal modes, i.e., with characteristic periodicities in imaginary\ntime.\n\nSo the situation is thoroughly muddled; there seems to be something\ndeep going on, but it\'s very unclear exactly what it is. Part of the\ndifference between the BTZ and Schwarzschild cases comes from the fact\nthat boundary conditions at infinity are different -- the BTZ black\nhole is asymptotically anti-de Sitter, not flat. This drastically\nchanges boundary conditions at infinity and therefore the quasinormal\nfrequencies, which by definition depend on those boundary conditions.\nThis is an indication that something\'s wrong, since the spacing of black\nhole states surely can\'t depend on details of geometry infinitely far\naway.\n\nOn the other hand, there are signs that Schwarzschild QNM frequencies\nshow up near the horizon in gravitational collapse, independent of\ndistant boundary conditions, so the modes *are* apparently capturing\nsome more local information. But what that local information is, we\ndon\'t know.\n\nSteve Carlip\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>John Baez <baez@galaxy.ucr.edu> wrote:

> But the real problem with this Hod-Dreyer idea of relating quasinormal
> modes to black hole entropy is not the SU(2) versus SO(3) business.
> It's that the idea doesn't seem to work for *rotating* black holes:

> Lubos Motl, Andrew Neitzke
> Asymptotic black hole quasinormal frequencies
> http://www.arXiv.org/abs/http://www.arxiv.org/abs/hep-th/0301173

To add to the confusion, though: the basic ``correspondence principle,''
as proposed by Bekenstein, *does* work for rotating (2+1)-dimensional
(BTZ) black holes. In fact, it works remarkably well -- it reproduces
not only parts of the basic structure of the asymptotic Virasoro algebra,
but also a piece of an underlying substructure that's been proposed as
a quantization of the boundary Liouville theory. See Birmingham, Carlip,
and Chen, http://www.arxiv.org/abs/hep-th/0305113, Class. Quant. Grav. 20 (2003) L239. But if
you look at the details of the correspondence, they look very different
from the Hod-Dreyer version.

To add even further to the confusion: a modified version of Bekenstein's
``correspondence principle'' also holds for several large classes of
near-extremal charged, rotating black holes of the sort that are fairly
well understood in string theory. These black holes have a near-horizon
geometry that looks like (BTZ)xS^n, and if you apply the correspondence
principle to the corresponding BTZ quasinormal frequencies, you get quite
a bit of correct information about the string theory description -- not
just the right quantization of energy and momentum flowing around the
black string, but even the right ``charge fractionization'' that's
usually explained in terms of branes wrapping around cycles more than
once. See Birmingham and Carlip, http://www.arxiv.org/abs/hep-th/0311090, Phys. Rev. Lett. 92
(2004) 111302. Again, though, the details look very different from the
Hod-Dreyer results. In fact, the relevant modes aren't even ordinary
quasinormal modes any more (they're quasinormal-like modes for the near-
horizon geometry, but require different boundary conditions at infinity).
We don't yet understand what they are, though they appear to be related
to thermal modes, i.e., with characteristic periodicities in imaginary
time.

So the situation is thoroughly muddled; there seems to be something
deep going on, but it's very unclear exactly what it is. Part of the
difference between the BTZ and Schwarzschild cases comes from the fact
that boundary conditions at infinity are different -- the BTZ black
hole is asymptotically anti-de Sitter, not flat. This drastically
changes boundary conditions at infinity and therefore the quasinormal
frequencies, which by definition depend on those boundary conditions.
This is an indication that something's wrong, since the spacing of black
hole states surely can't depend on details of geometry infinitely far
away.

On the other hand, there are signs that Schwarzschild QNM frequencies
show up near the horizon in gravitational collapse, independent of
distant boundary conditions, so the modes *are* apparently capturing
some more local information. But what that local information is, we
don't know.

Steve Carlip