I supposed that black holes must be strong thermal sources. This link
seems to confirm and gives a very interesting view of material in an
accretion disk the near area to a black hole.
If any reader has knowledge of the mechanism by which the infra-red is
made blue, I would appreciate a reference. The article itself does not
seem to cite a source.
> I supposed that black holes must be strong thermal sources. This link
> seems to confirm and gives a very interesting view of material in an
> accretion disk the near area to a black hole.
> If any reader has knowledge of the mechanism by which the infra-red is
> made blue, I would appreciate a reference. The article itself does not
> seem to cite a source.
The article talks about using a polarization filter to filter out scattered light from the outer regions so that what is left is the light from the inner regions. The colours themselves are "false colours".
Infrared light is not visible, so one can use arbitrary colours to indicate different wavelength. This is done in all wavelength bands: if you see an image based on radio waves, then different colours can be used to indicated different radio wavelengths.
>I supposed that black holes must be strong thermal sources. This link
>seems to confirm
No, it does not. It's talking about the disks around accreting black
holes, not the black holes themselves.
>If any reader has knowledge of the mechanism by which the infra-red is
>made blue, I would appreciate a reference. The article itself does not
>seem to cite a source.
'blue color of the disk in infrared light' refers to the ratio of
emission at short wavelengths to long wavelengths: this would be a
consequence of the temperature and emissivity structure of the disk.
Martin
-- Martin Hardcastle
School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK
Please replace the xxx.xxx.xxx in the header with herts.ac.uk to mail me
> 'blue color of the disk in infrared light' refers to the ratio of
> emission at short wavelengths to long wavelengths: this would be a
> consequence of the temperature and emissivity structure of the disk.
> Martin
Exactly, I assume the false blue color does represent shorter wave-
lengths and thus higher temperature. As the stronger g field near the
holes should red-shift emissions, not blue shift them.
I realize I may be mistaken, that is why I would like to refer to the
model, mentioned in the article but not cited therein that made the
prediction of the disk these researchers have now observed.
I am attempting to understand the relation between kinetics and
radiated heat. The baseline assumption is that emissions cool
temperature and reduce kinetics. In accord with Max Plank's original
and now much confirmed hypothesis.
I do not much care if the heat source is believed to be directly from
the hole itself or from the accretion disk around the hole.
I personally have observed experimental results that clearly indicate
that heat preferentially radiates or otherwise travels UP. This I
believe to be in direct contrast to the behavior of general electro-
magnetic radiation which preferentially curves downward in a
gravitational field.
As a result of these observations, I personally, would not be
surprised to find that black holes themselves emit heat, in spite of
the fact that such a finding might be considered to be in conflict
with common understandings of some excellent theories.
Black holes indisputably have strong gravitational fields and vigorous
kinetics and these in and of themselves can create heat from in
falling material, this effect, I assume is the predicted source of the
blue (yes,false color, blue) disk, I would simply like to reference
the model that made this prediction.
If I were looking for confirmation of the Suposition that black holes
can themselves can emit heat, a noisy source like the source observed
in this article would be a poor choice. There are however large scale
voids presently observed and cataloged. If these structures do, or
did, contain fully mature black holes that have previously consumed
all the matter energy that a person might otherwise expect to be in
these regions and if these hypothetical black holes were observed to
be visible in infra-red telescopy, I would take that as an possible
confirmation of my conjecture that heat may escape black holes even
when nothing else does.
Meanwhile, the well accepted models that show black holes radiating
via their accretion still makes black holes strong thermal sources, as
evidenced by their effects on nearby gas and dust.
The energetic balance of Black Holes is of interest because both the
matter and radiant energy bound within the Hole are a source of
negative entropy.
To Newtonian physics a violation of conservation. Relativity makes
things a bit better, in that the mass/energy that has gone dark can be
understood, and perhaps even accounted for, BUT, this negative entropy
seems to me to be a possible violation of the Equivalence Principle as
well.
The mass/energy that has gone dark is not necessarily gone, it is just
that the only observable related to all this mass energy is its effect
on the stress-energy tensor globally and the metric tensor locally.
The very effects that make the mass/energy dark but indirectly
observable.
If the mass energy is still present, but unobservable, which is my
interpretation. Then the deformation of the stress-energy and metric
tensors observed are not equivalent to the hidden mass/energy within.
Creating the appearance of an equivalence violation, if not a
violation in fact.
This, could be an important finding. It may, or may not, have a
parallel in Quantum Theory in the elusive Higg's Boson. If it becomes
demonstrable that the mass defect currently attributed to the Higg's
Boson is actually a Schwarzshild type observational limit, then the
stress energy actually present whithin the nucleus may only be
directly observed nearly at, or below this limit, or indirectly
observed as a excess of kinetic energy upon some types of nuclear
decay.
If there is a parallel, then current indirect, possibly thermally
based, observation techniques for nuclei, like NMRI might be refined
or improved through better theoretical modelling. Specifically, the
polarizing filter of this article, simply filters the strong but
chaotic thermal noise to extract the perhaps more meaningful accretion
disk signal. Thus this same polarizing filter technique could prove a
useful NMRI technique as well.
Meanwhile, only a reference to the model that made the prediction
about the Black Hole disk will allow me to make an estimates of the
strength of this long anticipated but only recently confirmed thermal
source.
I find I am quite interested in this question and if it turns out
nobody in this forum knows of the source of the model, then I believe
I shall write the author's and hope they are willing to respond to my
questions.
> >I supposed that black holes must be strong thermal sources. This link
> >seems to confirm
> No, it does not. It's talking about the disks around accreting black
> holes, not the black holes themselves.
Right. Black holes do emit Hawking radiation, but the MORE massive the black hole, the LOWER its temperature. Thus, only very small ones emit much thermal radiation, but they quickly radiate themselves away. So, a black hole with high temperature due to Hawking radiation over a long period of time can't exist. There is no other mechanism via which black holes could radiate.
Often, the distinction between black holes and their environment, in particular accretion disks and matter falling into them, is not clear in some popular accounts.
> 'blue color of the disk in infrared light' refers to the ratio of
> emission at short wavelengths to long wavelengths: this would be a
> consequence of the temperature and emissivity structure of the disk.
Right. It is not literally blue, since infrared light is invisible.
"Red" and "blue" are often used to denote longer and shorter
wavelengths, respectively, and images from non-visible bands are often
shown in "false colours" using this scheme, often choosing three bands
and assigning them to visual primary colours to produce a "false-colour" image.
In article
<230e29fc-d070-4985-b9fe-99a7804a9...@t8g2000yqd.googlegroups.com>,
"Anon E. Mouse" <agall...@gmail.com> writes:
> Exactly, I assume the false blue color does represent shorter wave-
> lengths and thus higher temperature. As the stronger g field near the
> holes should red-shift emissions, not blue shift them.
Yes, but the gravitational redshift is too small to play a role here.
The emission is coming from outside the event horizon (of course).
> I personally have observed experimental results that clearly indicate
> that heat preferentially radiates or otherwise travels UP.
What are these results?
> This I
> believe to be in direct contrast to the behavior of general electro-
> magnetic radiation which preferentially curves downward in a
> gravitational field.
What do you mean by heat? If radiation, then that is electromagnetic radiation. If you are thinking of convection then, yes, it might move up since the medium expands and is lighter than what is cooler.
> As a result of these observations, I personally, would not be
> surprised to find that black holes themselves emit heat, in spite of
> the fact that such a finding might be considered to be in conflict
> with common understandings of some excellent theories.
You need some evidence to back this up.
> Black holes indisputably have strong gravitational fields and vigorous
> kinetics and these in and of themselves can create heat from in
> falling material, this effect, I assume is the predicted source of the
> blue (yes,false color, blue) disk, I would simply like to reference
> the model that made this prediction.
Search the literature for accretion disks. I think Donald Lynden-Bell might have been the first to explicitly calculate this.
> If I were looking for confirmation of the Suposition that black holes
> can themselves can emit heat, a noisy source like the source observed
> in this article would be a poor choice. There are however large scale
> voids presently observed and cataloged. If these structures do, or
> did, contain fully mature black holes that have previously consumed
> all the matter energy that a person might otherwise expect to be in
> these regions and if these hypothetical black holes were observed to
> be visible in infra-red telescopy, I would take that as an possible
> confirmation of my conjecture that heat may escape black holes even
> when nothing else does.
Voids do not arise because black holes ate up the stuff which used to be there. Far from a black hole, it looks like any other mass. Close in, yes, it can swallow things, but the timescale is much too long.
> To Newtonian physics a violation of conservation. Relativity makes
> things a bit better, in that the mass/energy that has gone dark can be
> understood, and perhaps even accounted for, BUT, this negative entropy
> seems to me to be a possible violation of the Equivalence Principle as
> well.
Please explain.
> This, could be an important finding. It may, or may not, have a
> parallel in Quantum Theory in the elusive Higg's Boson. If it becomes
> demonstrable that the mass defect currently attributed to the Higg's
> Boson is actually a Schwarzshild type observational limit, then the
> stress energy actually present whithin the nucleus may only be
> directly observed nearly at, or below this limit, or indirectly
> observed as a excess of kinetic energy upon some types of nuclear
> decay.
> Voids do not arise because black holes ate up the stuff which used to be
> there. =A0Far from a black hole, it looks like any other mass. =A0Close i=
n,
> yes, it can swallow things, but the timescale is much too long.
> > To Newtonian physics a violation of conservation. Relativity makes
> > things a bit better, in that the mass/energy that has gone dark can be
> > understood, and perhaps even accounted for, BUT, this negative entropy
> > seems to me to be a possible violation of the Equivalence Principle as
> > well.
> Please explain.
> > This, could be an important finding. It may, or may not, have a
> > parallel in Quantum Theory in the elusive Higg's Boson. If it becomes
> > demonstrable that the mass defect currently attributed to the Higg's
> > Boson is actually a Schwarzshild type observational limit, then the
> > stress energy actually present whithin the nucleus may only be
> > directly observed nearly at, or below this limit, or indirectly
> > observed as a excess of kinetic energy upon some types of nuclear
> > decay.
> Please explain.
In an EFE model of a black hole the mass/energy contained within the
Swartzschild demonstrates its existence by the ongoing deformation of
the stress energy tensor causing closed field lines and unobservable
matter and light.
If the mass/energy were truly gone so would be the distortion of the
stress-energy and metrics. I.e. no lensing.
Since the mass/energy is there - a fact demonstrated by the on going
lensing, the heat, e/m, mass and kinetic energies are there also - a
reasonable inference, based on theory.
None the less these energies can not be directly observed and so an
simple accounting would show a mass/energy deficit.
An inferential accounting based on EFE theory could produce a better
estimate, but...
If gravitation propagates according to realtivistic limits then a
great deal of stress-energy is also globally unaccounted. Thus, all
the recognized forms of energy according to EFE become invisible to
direct observation, distorting the proper accounting by creating a
shortage which could be represented by an entropy term. However, there
is presently no such entropy term in the EFE. Thus, I infer there may
be an issue with the completeness of the EFE and further I begin to
identify the character of that incompleteness.
If, black holes continuously accumulate mass/energy/entropy then the
Equivalence principle is not just damaged in a way that an entropy
term could possibly repair, instead it is actually broken. On the
other hand if heat energy can escape black holes then equivalence is
possibly still preserved.
As to a mechanism for heat transfer that does not in and of itself
violate EFE... If there is molecular kinetic motion inside the
Swartzshild radius then the black body radiations associated with the
cooling of this matter and its loss of kinetic energy contributing to
its bound condition could radiate upward with decreasing frequency and
when absorbed increase the kinetics of a higher orbital molecule. This
process can be repeated causing a fairly uniform heating and kinetic
for the in falling matter with a very large amount of radiant heat
escaping, the Schartzshild radius via thermal tunneling. Some quantity
of this composite energy may have started as visible light, but can
only escape at much lower wave-lengths, however these lower
frequencies when absorbed simply increase higher orbital kinetics and
so on. Florescent lights perform this a protion of this trick all the
time. I also observe that in the image of the accretion disk in
reference paper the false blue color is quite uniform. A shocking
observation if only gravitation and kinetics are involved, as a bright
blue/white center is what I would predict, if and only if thermal
radiant pressure were not present.
In terms of QFT;
Nuclei exhibit somewhat similar characteristics. The energetic
accounting is off, in comparison to "normal" matter. Binding energies
are anomalously great in relation to the kinetics of the broken pieces
leading to mass deficits of various types. These deficits are
typically not dealt with as entropy in current theory, but the
particles that fill this hypothetically entropic niche are
persistently not observed.
I began this thread as a search for better models and terminology and
I do sincerely lack both the mathematical frame work and proper terms
to explain this hypothesis more fully than this. I apologize for this
limitation on my part and I again thank those who are commenting.
I will reference the authors you mention and see if this model
provides any helpful material.
In article <230e29fc-d070-4985-b9fe-99a7804a9...@t8g2000yqd.googlegroups.com>,
Anon E. Mouse <agall...@gmail.com> wrote:
>I realize I may be mistaken, that is why I would like to refer to the
>model, mentioned in the article but not cited therein that made the
>prediction of the disk these researchers have now observed.
The press release does in fact give details of the paper that it's
based on. You can find all the information you need here:
In article
<e0e4ddeb-0091-47d0-b641-28b2a0f58...@e18g2000yqc.googlegroups.com>,
"Anon E. Mouse" <agall...@gmail.com> writes:
> In an EFE model of a black hole the mass/energy contained within the
> Swartzschild demonstrates its existence by the ongoing deformation of
> the stress energy tensor causing closed field lines and unobservable
> matter and light.
> If the mass/energy were truly gone so would be the distortion of the
> stress-energy and metrics. I.e. no lensing.
Does anyone claim it is "truly gone"?
> Since the mass/energy is there - a fact demonstrated by the on going
> lensing, the heat, e/m, mass and kinetic energies are there also - a
> reasonable inference, based on theory.
There is a theorem which states that a black hole has 3 and only 3 properties: mass, charge and angular momentum.
"Anon E. Mouse" <agall...@gmail.com> wrote in message [[Mod. note -- 107 excessively-quoted lines snipped here. -- jt]]
" I personally have observed experimental results that clearly indicate
that heat preferentially radiates or otherwise travels UP. This I
believe to be in direct contrast to the behavior of general electro-
magnetic radiation which preferentially curves downward in a
gravitational field."
Would not Hawking radiation produce just such an effect?
The "escaping" particle's momentum surely must be high and pretty much straight up to actually escape.
[[Mod. note -- Hawking radiation has a thermal (black-body) spectrum.
Offhand, I don't know its angular distribution.
-- jt]]
[Moderator's note: My apologies for the delay; this post ended up in the wrong email folder for some reason. -P.H.]
On 6/1/12 6/1/12 - 2:08 AM, Anon E. Mouse wrote:
>>> To Newtonian physics a violation of conservation. Relativity makes
>>> things a bit better, in that the mass/energy that has gone dark can be
>>> understood, and perhaps even accounted for, BUT, this negative entropy
>>> seems to me to be a possible violation of the Equivalence Principle as
>>> well.
Hmmm. In GR, a Schwarzschild black hole contains no matter. It is simply
a configuration of the fields (metric) that is static and satisfies the
field equation with reasonable boundary conditions. Energy-momentum
conservation is satisfied throughout the manifold (including inside the
horizon).
If one adds an infalling spherically symmetric mass shell to Schw.
spacetime, then the shell intersects the singularity in finite proper
time, and once it intersects the singularity the manifold is isometric
to a higher-M Schw. manifold [#]. For a solar-mass black hole, the
proper time between crossing the horizon and intersecting the
singularity is on the order of a microsecond.
[#] Speaking loosely; this is difficult to specify precisely.
>>> This, could be an important finding. It may, or may not, have a
>>> parallel in Quantum Theory in the elusive Higg's Boson. If it becomes
>>> demonstrable that the mass defect currently attributed to the Higg's
>>> Boson is actually a Schwarzshild type observational limit, then the
>>> stress energy actually present whithin the nucleus may only be
>>> directly observed nearly at, or below this limit, or indirectly
>>> observed as a excess of kinetic energy upon some types of nuclear
>>> decay.
This Higgs boson in the standard model of particle physics is COMPLETELY
DIFFERENT.
> In an EFE model of a black hole the mass/energy contained within the
> Swartzschild demonstrates its existence by the ongoing deformation of
> the stress energy tensor causing closed field lines and unobservable
> matter and light.
Hmmm. You are confused, or at least using words funny. The Schwarzschild
and Kerr manifolds have T=0 everywhere, including inside the horizon of
the black hole. That is, they have no mass/energy ANYWHERE.
Manifolds with a black hole and infalling matter have T!=0 for a while,
but ultimately they also have T=0 everywhere [#], with the exception of
an EM field in the case of a black hole with net charge -- in general
that is VASTLY smaller than the "mass" one would assign to the black
hole from distant measurements of its gravitation.
Note that it is not clear that one can describe the singularity as
"inside" the black hole, as it is not part of the manifold and such
relationships only apply to the manifold. Colloquially we say that it is
"inside the black hole", but this is certainly loosely stated and has
problems when analyzed closely.
Consider the limit points of all geodesics intersecting the
singularity of Schw. spacetime. They are certainly inside the
horizon. But the singularity is not its limit points....
> If the mass/energy were truly gone so would be the distortion of the
> stress-energy and metrics. I.e. no lensing.
Not so. The field equation applies, and it permits the gravitation of a
black hole to persist even though it "contains" no mass/energy (same
caveat as for "inside" above).
> Since the mass/energy is there
WHERE????? Having a location implies it is localizable in the manifold,
but it isn't.
Bottom line: black holes are WEIRD, and common language is inappropriate
for them. Because, of course, that language evolved without knowledge of
them. Beware of colloquialisms that don't actually reflect the math or
actual structure of the manifold.
> - a fact demonstrated by the on going
> lensing, the heat, e/m, mass and kinetic energies are there also - a
> reasonable inference, based on theory.
Not GR. In GR the metric of a vacuum manifold can have a configuration
with gravitation, such as Schw. and Kerr.
> If gravitation propagates according to realtivistic limits then a
> great deal of stress-energy is also globally unaccounted.
Non sequitur.
> Thus, all
> the recognized forms of energy according to EFE become invisible to
> direct observation, distorting the proper accounting by creating a
> shortage which could be represented by an entropy term. However, there
> is presently no such entropy term in the EFE. Thus, I infer there may
> be an issue with the completeness of the EFE and further I begin to
> identify the character of that incompleteness.
You are ignoring boundary conditions. Every differential equation
requires them, and the field equation is no exception. The "stuff" you
seem to think is "missing" is actually outside the boundary of the
manifold. Yes, that is "missing" in some sense, but not in all senses.
Once boundary conditions are included (as they must be), I see no issue
with the "completeness of the EFE".
> If, black holes continuously accumulate mass/energy/entropy then the
> Equivalence principle is not just damaged in a way that an entropy
> term could possibly repair, instead it is actually broken. On the
> other hand if heat energy can escape black holes then equivalence is
> possibly still preserved.
This does not apply to GR.
> As to a mechanism for heat transfer that does not in and of itself
> violate EFE... If there is molecular kinetic motion inside the
> Swartzshild radius then the black body radiations associated with the
> cooling of this matter and its loss of kinetic energy contributing to
> its bound condition could radiate upward with decreasing frequency and
> when absorbed increase the kinetics of a higher orbital molecule.
No. Inside the horizon of a Schw. black hole, no timelike or null
trajectory ever goes to higher "radius" (in the sense of closer to the
horizon or further from the limit points of the singularity). I'm pretty
sure that similar conditions apply to all black-hole manifolds.
Stated differently: every spherical surface inside the horizon is a
closed trapped surface; the horizon is merely the outermost one.
> and a freely available copy of the paper can be found by going to
> 'arxiv e-print' and then 'PDF'.
> The predictions on the temperature structure of accretion discs go
> back to the work of Shakura and Sunyaev in the 1970s.
> Martin
> --
> Martin Hardcastle
> School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK
Thank you Martin.
With your assistance I was able to find the paper cited in the Paper
of interest. It is quite detailed. From this source I was able to
confirm that the black holes are indeed modeled and observed to be
extremely hot black body sources and I found that the rather flat blue
spectra is believed to be the result of electron scattering in the
outer layers of the accretion.
http://arxiv.org/abs/astro-ph/9911317 Non-LTE Models and Theoretical Spectra of Accretion Disks in Active
Galactic Nuclei. III. Integrated Spectra for Hydrogen-Helium Disks
The peak temperatures predicted by some of these models are north of
36kK. Quite hot indeed. The radiation energies of the disks themselves
are not enough to achieve or sustain these temps and the model paper
cites gravitational radiation as the heat source.
If the space-time field lines of the hole itself are spatially closed,
then the approach to the hole would become a tachyon vector field
which matches up with the observed disk kinetics, Increased kinetics
due to radiation pressure.
However, if the hole itself is viewed as a enormously powerful
compressor, then the accumulate kinetic energy would be similarly
large. Either this energy is missing as entropy, an non LTE effect, or
it escapes as heat. I personally think the evidence of high
temperature around black holes indicates thermal radiation (black-
body) behaves differently than other photon type energy. I see no
other viable solution. In terms of standard EFE theory there should be
closed field lines in the Stress-Energy tensor term of approximately
equal magnitude to the metric and Rikki tensor combined and this
energy should be just almost as invisible as the mass or light.
The thermal tunneling effect I mentioned previously can only work
through the kinetics of the disk and not all black holes are quasars.
They are not all Kerr type, and so for these there is no obvious to me
means by which a black hole could express its heat by interaction with
its surroundings.
I apologize for the speculative nature of this inference.
> > In an EFE model of a black hole the mass/energy contained within the
> > Swartzschild demonstrates its existence by the ongoing deformation of
> > the stress energy tensor causing closed field lines and unobservable
> > matter and light.
> AAG
> Hmmm. You are confused, or at least using words funny. The Schwarzschild
> and Kerr manifolds have T=0 everywhere, including inside the horizon of
> the black hole. That is, they have no mass/energy ANYWHERE.
> Tom Roberts--
Outside the Schwr. radius no mass/energy is directly observable. This
is NOT the same as, "they have no mass/energy ANYWHERE."
Your argument seems to rest on the proposition that if the math works
out - the physics equivalence/conservation doesn't matter.
If the Schwr. radius is treated as a spherical volume containig a very
great mass density that causes this radius to collapse to a
singularity then the existence of the mass can be inferred and its
invisibility is explained.
The - there is no mass hypothesis demands that the stress-energy field
lines collapse into a singularity for no particular physical reason.
This seems to me an unlikely supposition.
I do not feel I am ignoring the bound condition. I am simply treating
it as a boundary. A boundary between externally observable space-time
and externally unobservable space-time.
You hypothesis treats the Schwr. radius as the line dividing normal
space-time and a magical kingdom.
AAG
> Manifolds with a black hole and infalling matter have T!=0 for a while,
> but ultimately they also have T=0 everywhere [#], with the exception of
> an EM field in the case of a black hole with net charge -- in general
> that is VASTLY smaller than the "mass" one would assign to the black
> hole from distant measurements of its gravitation.
> Note that it is not clear that one can describe the singularity as
> "inside" the black hole, as it is not part of the manifold and such
> relationships only apply to the manifold.
> > Tom Roberts--
I agree. Since the manifold collapses to a singularity and the hole
exhibits gravitation indicating mass - demonstrating the probable
existence of space-time within the singularity I believe it is more
correct to describe this duality as a super-position.
> Not so. The field equation applies, and it permits the gravitation of a
> black hole to persist even though it "contains" no mass/energy (same
> caveat as for "inside" above).
I believe a more accepted interpretation of this type of computational
result is the D membrane of string theory. This represents the
gravitation of the hole as a dimple in the manifold and the region
bound within the singularity as the oblate spheroid of a letter D
laying on its face. (A 2d sectional view of an inverted 5d manifold.)
The super-position can also be dealt with as a dot product inversion -
i.e. a superposition of space-time and time-space or a temporal
inversion within the manifold of the singularity. Mathematically,
these are both correct and they are not mutually exclusive. The dot
product transposition (matrix inversion) is a 4 or 5d representation
and the temporal inversion is a 2 or 3d representation
AAG
[[Mod. note -- Tom Roberts is right: Schwarzschild spacetime has a
zero stress-energy tensor everywhere (i.e., at all events with r > 0).
Any decent introductory GR book will contain a proof of this -- it's
a straightforward (although somewhat tedious) mathematical calculation.
Moreover, the event horizon (r = 2M) isn't a boundary of Schwarzschild
spacetime. This is easily seen if you work in Kruskal-Szekeres
coordinates, where the metric is manifestly regular and nonsingular
at r = 2M.
[Note that r = 0 isn't part of Schwarzschild spacetime.
That is, in terms of the classical Einstein equations,
r = 0 isn't part of the differentiable manifold which
we call "Schwarzschild spacetime", so we can't define
spacetime curvature or compute a stress-energy tensor
there. Loosely speaking, asking what happens at r=0 is
sort of like asking what happens to a Dirac delta function
$\delta(x)$ at x=0, i.e., it's not mathematically defined.
Physically, we believe (but don't know for sure) that
the Einstein equations don't correctly describe gravitation
at very small r in Schwarzschild spacetime. That is, at
very small r quantum-gravity effects become important.
Since we don't (yet) have a working theory of quantum
gravity, we don't know what happens at very small r.]
However, there are (many) other spacetimes (e.g., those where matter
is collapsing and has just recently formed a black hole) which coincide
with (more precisely, are isometric to) Schwarzschild spacetime outside
the horizon, but which have (time-dependent) stress-energy tensors
which are nonzero at some events inside the horizon. See Misner, Thorne,
& Wheeler for details. (Alas My MTW is packed away & inaccessable right
now, so I can't give a chapter/section reference.)
As Tom Roberts said, such a spacetime will very quickly (I think
within at most a few light-crossing times of the Schwarzschild radius)
evolve into Schwarzschild spacetime (with zero stress energy tensor
for all r > 0).
More generally, knowing that a spacetime is isometric to Schwarzschild
spacetime outside r = X (for some X > 0) does *not* suffice to uniquely
determine the spacetime inside r = X.
-- jt]]
>>Anon E. Mouse wrote:
>>> In an EFE model of a black hole the mass/energy contained within the
>>> Swartzschild demonstrates its existence by the ongoing deformation of
>>> the stress energy tensor causing closed field lines and unobservable
>>> matter and light.
> Tom Roberts wrote:
>> Hmmm. You are confused, or at least using words funny. The Schwarzschild
>> and Kerr manifolds have T=0 everywhere, including inside the horizon of
>> the black hole. That is, they have no mass/energy ANYWHERE.
> Outside the Schwr. radius no mass/energy is directly observable. This
> is NOT the same as, "they have no mass/energy ANYWHERE."
Yes, they are not the same. But as I said, for the Schwarzschild and Kerr manifolds, BOTH are true.
For a manifold in which a spherically symmetric collapse occurs, there
is a region in which there is mass/energy present somewhere in the
manifold, and there is a region that is isometric to a corresponding
region of Schwarzschild spacetime; if you wait long enough, then like
the Schw. manifold there is no mass/energy anywhere. In this latter
region one might like to claim "there is mass/energy in the
singularity", but that is really using a pun on the word "in" -- "in" is
an inclusive relation, which only applies in the manifold where such
inclusion is possible; the singularity is not part of the manifold. This
is a case where the English language cannot accurately represent the
mathematics. Or, presumably, the physics.
> Your argument seems to rest on the proposition that if the math works
> out - the physics equivalence/conservation doesn't matter.
No. Conservation of energy applies at every point of the manifold (i.e.
D_i T^ij = 0). the equivalence principle also applies at every point of
the manifold (i.e. Riemann normal coordinates can be constructed). But
note that we have no theory that applies outside the manifold, so we
cannot really discuss what happens there. Moreover, very close to a
singularity (in the manifold) it seems likely that GR is no longer a
good model, but in the absence of a theory of quantum gravity we don't
know how to formulate a better model that applies there.
> If the Schwr. radius is treated as a spherical volume containig a very
> great mass density that causes this radius to collapse to a
> singularity then the existence of the mass can be inferred and its
> invisibility is explained.
Your words are garbled. the "radius" does not "collapse" at all, it is
the MATTER which collapses; the Schw. radius remains constant.
> The - there is no mass hypothesis demands that the stress-energy field
> lines collapse into a singularity for no particular physical reason.
GRAVITY is the "reason". More accurately, once any timelike object is
inside the Schw. radius, its worldline inevitably intersects the
singularity in a finite proper time (microseconds for a 1 solar mass
black hole). Once it does that, we have no theory that applies, and thus
no idea of what "happens".
> This seems to me an unlikely supposition.
Then you need to improve your sense of what happens in GR.
> You hypothesis treats the Schwr. radius as the line dividing normal
> space-time and a magical kingdom.
Note at all. This is not "my hypothesis", I have been giving a
description of the Schwarzschild manifold, and other manifolds, in GR.
The Schw. radius is NOT any boundary, it is merely the outermost closed
trapped surface in the manifold. Nothing "magical" occurs inside, it's
just that all future-pointing nonspacelike paths are directed inward
(note this is a continuous evolution from the nonspacelike paths
immediately outside).
>> The field equation applies, and it permits the gravitation of a
>> black hole to persist even though it "contains" no mass/energy (same
>> caveat as for "inside" above).
> I believe a more accepted interpretation of this type of computational
> result is the D membrane of string theory.
Not among any physicists I know (most of whom are HEP experimentalists
and theorists, not string theorists). String theory is viewed as HIGHLY
speculative and far from established. On the other hand, GR is well
established, with the caveat that it does not apply at small scales, and
there are questions about how it applies at very large scales (dark
matter and dark energy are basically viewed as gaps in our knowledge of
matter, not as failures of GR).