Schw. black hole ringing frequencies

[marcus]

topic of BH ringing freq. came up in "Loop Quantum Gravity" thread in SringBraneLQG forum.
I'm starting this thread here in hopes that some regulars here (Labguy, Nereid, others?) can shed additional light.

From a pedagogical or intuitive point of view it seems to bring the topic closer to home to notice that the ringing frequency of an ordinary BH with mass of sun would be an actual recognizable pitch in the soprano range.

A BH with four to five solar masses would ring with a frequency around middle D, which is near the high end of the bass range, so I could sing it.

The first major paper about this was Shahar Hod
http://arxiv.org/gr-qc/9812002
and two occasional PFers have contributed
(Lubos Motl, Andy Neitzke)
to what is a growing bunch of papers on BH "quasinormal modes"

But my focus here is not on "what's the latest and greatest news
about BH vibrations?" but rather just getting used to them
in a down-home way.

In the literature the prevailing practice is to use ANGULAR FORMAT for
frequencies----the symbol being omega instead of f. This in itself
takes a little getting used to.
It means that the A above middle C on the piano is 880pi
instead of 440.
But there are longterm benefits to getting accustomed to thinking frequencies in angular format (like, you get to use hbar whenever you want)

 

[marcus]

the formula

the formula for the frequency is

$$\frac{log3}{8\pi M}$$

where M is the mass of the hole

it looks clean expressed in natural units like this
so I won't put in the G and hbar and c
--------------------------

in Planck units the solar mass is 0.915 x 10³⁸
and middle D on the piano is 10^-40
these are two useful landmarks to remember
and in this situation they let you get the pitch
of a solar mass hole without much to-do.

$$\frac{log3}{8\pi 10^{38}}= 4.37 * 10^{-40}$$

roughly two octaves above middle D.

Now I see I left out the 0.915 so let's divide that in
and get 4.78 instead of 4.37

so to "hear" a solar mass black hole we just need to figure
out how many notes above middle D on the piano
the ratio 4.78 means. anybody?

 

[wolram]

i don't intend to add anything to this thread, but i thought
an audio sample may be of interest.



http://cfa-www.harvard.edu/seuforum/explore/blackhole/L3/smallholes.htm

A spinning black hole causes the fabric of space around it to actually vibrate. These vibrations in turn cause light emitted from near the black hole to pulse brighter and dimmer. NASA's Rossi X-ray Timing Explorer has actually captured these "black hole vibrations" — and researchers have converted them into sound. You can hear them by clicking here. (Allow a few seconds for sound file to download.) To learn more, click here.

 

[marcus]

Originally posted by wolram
i don't intend to add anything to this thread, but i thought
an audio sample may be of interest.
http://cfa-www.harvard.edu/seuforum/explore/blackhole/L3/smallholes.htm

...

thanks, it certainly is an interesting link. I followed it to
a page with some diagrams and explanation:

http://heasarc.gsfc.nasa.gov/docs/xte/learning_center/discover_0198.html

 

[marcus]

Recapping from previous post:
----------------------------------------
the formula for the frequency is

$$\frac{log3}{8\pi M}$$

where M is the mass of the hole

--------------------------

in Planck units the solar mass is 0.915 x 10³⁸
and middle D on the piano is 10^-40
these are two handy landmarks
in this situation they let you get the pitch
of a solar mass hole

$$\frac{log3}{8\pi (0.915*10^{38})}= 4.78 * 10^{-40}$$

a bit more than two octaves above middle D.

so to "hear" a solar mass black hole we just need to figure
out how many notes above middle D on the piano
the ratio 4.78 means.
-----------------------

4.78 means 2 octaves and 3 halfsteps
so you go to a D that is two octaves above middle D
and then 3 halfsteps to F
D D# E F

so the resonant frequency of a solarmass black hole is an F
------------------------

LPF and I went thru the calculation in a parallel thread
in MathScience Philosophy forum, so I'm just tying loose ends up here.

one way to analyze the 4.78 is to use the ln key on the calculator
ln 4.78 divided by ln 2
is 2.257
that says 2 octaves plus however many halfsteps you get by
multiplying 0.257 by 12
(which is about 3, call it 3 for round numbers)

 

[Silverious]

This may be a silly question, and I'm probably going in over my head, but, if a black hole does create sound, would we even be able to hear it?

 

[marcus]

Originally posted by Silverious
This may be a silly question, and I'm probably going in over my head, but, if a black hole does create sound, would we even be able to hear it?

the people who write about the "quasinormal mode" frequencies sometimes call them "ringing" frequencies
but I think this is metaphorical
in a vacuum there can be no sound, as we understand sound

I guess the idea is the BH is a structure with some rigidity and it can be impacted, say by a chunk of matter falling in
some asymmetric impact would disturb the BH
like a hammer-blow on one side of a big bell
and it would shiver or vibrate briefly, like a bell, from
this disturbance

but we would not hear this
because there could be no air to bring the sound to us
all the air would have been already sucked into the hole!
so even if it vibrates like a bell, it does not make any sound

 

[Silverious]

If the BH does vibrate when impacted, where does the energy go? Can it actually leave the event horizon?

 

[marcus]

there is a split between classical analysis and quantum analysis which is bridged by the "Bohr correspondence principle" which says roughly this:

if you analyse a system classically (like some Victorian gentleman, Maxwell, Helmholz, of the late 19th C) and you see vibrations

then you can expect that these vibrations correspond to transitions between energy levels in the quantized version.

so classical vibrations correspond to quanta
but the actual connection seems a mite vague

Still, there is Hawking radiation and according to LQG the area is quantized in discrete steps
and the area can increase by one step (as the hole absorbs energy and increases in mass) and it can decrease by one step (as the hole radiates energy and decreases in mass)

and this tiny step in energy is postulated (by Shahar Hod and people who go along with him) to be related, by the Bohr correspondence principle, to the ringing frequency found by analysing the system classically.

Cant tell you much more. Do you want links? Or maybe someone else will drop in and explain further.

 

[ranyart]

Originally posted by marcus
there is a split between classical analysis and quantum analysis which is bridged by the "Bohr correspondence principle" which says roughly this:

if you analyse a system classically (like some Victorian gentleman, Maxwell, Helmholz, of the late 19th C) and you see vibrations

then you can expect that these vibrations correspond to transitions between energy levels in the quantized version.

so classical vibrations correspond to quanta
but the actual connection seems a mite vague

Still, there is Hawking radiation and according to LQG the area is quantized in discrete steps
and the area can increase by one step (as the hole absorbs energy and increases in mass) and it can decrease by one step (as the hole radiates energy and decreases in mass)

and this tiny step in energy is postulated (by Shahar Hod and people who go along with him) to be related, by the Bohr correspondence principle, to the ringing frequency found by analysing the system classically.

Cant tell you much more. Do you want links? Or maybe someone else will drop in and explain further.

It is interesting that for certain frequencies can be seen at close range but disappear as one moves farther and farther away
http://www.bartleby.com/65/mo/modulat1.html

Now the ringing correspondence for Blackholes need to be detected in a certain bandwidth, the 'Graviton' Width may be akin to the Phase 'in'-'out' which accumalates over ever increasing distances, and diminishes at De-creasing distances.

This may seen strange that Gravitons opperate by an Entangled state of (inner-graviton) and its coupled (outer-graviton). But there is a reason why Gravitons 'Correspond' only at finite/infinite distances, again the 'wave-function collapse' seems to have a baring on Quantum Systems and Relative Systems.

The far away 'observer' in Blackhole Mechanics is shrouded within a Graviton 'horizon', this has 'Directional' consequences as well as Prefered Dependant consequences.

When one moves outwards from a Quantum 'Quanta' frame (Bohr-Frame) the continuous journey reaches a limit, a crossover point, one can say this happens with a lower-bound (Quarks) and an upper bound for a certain amount of visible Matter (atomic-dust-visible).

In the Absence of 'MATTER', space is continuous, wherby the 'APPEARENCE' of matter is the DISCONTINUNESS! or bits of space no longer continue when a Proton appears in its entirety, which according to Bohr, if one strips a Proton down to its lower bounds, then space you are detecting appears as a Quantum Continuity, Field.

Its the presence of Matter that disects Space, if one looks at the Galaxies out in Space, they have no Matter between them, they Have a Quantum Field, a continuous Field of Broken up Protons energy, Electromagnetic Vaccum Field. This is the domain of Graviton Dispersion form Galaxy to Galaxy. Some Galaxies have High signals because the Phase Modulation is such that they produce increased 'overtones':http://www.bartleby.com/65/tu/tuningsy.html

Dimensionally speaking of Course, we are somewhere between a Perfect 'Third', and Embedded in a Perfect 'Fifth'?