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Solkar
Anmeldedatum: 29.05.2009
Beiträge: 293
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 Verfasst am: 11.07.2009, 00:43 Titel: |
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Hi Erik!
Your approach
| Erik hat Folgendes geschrieben: | | $[...]M^2_4\int dx {R_4\over 2}\sqrt{-g_4}\ \ = \ \ M^{D-2}_D \int dy e^{2A}\sqrt{g_{D-4}} \int dx \sqrt{-g_4} {R_4(x)\over 2} + O(V_4)$ |
My approach
| Solkar hat Folgendes geschrieben: | | $\Rightarrow \frac{M_4^2}{M_D^{D-2}} = \frac{\int d^4x \int \frac{d^{D-4}x}{{(2\pi)}^{D-4}}\sqrt{g_{D-4}} e^{2A} \sqrt{-g_4} \mathcal{R}_4} {\int d^4x \sqrt{-g_{4}}\mathcal{R}_4}$(VII.7) |
Aside of the fact that there's an obvious resemblence  ,
| Erik hat Folgendes geschrieben: | | Dividing by something that is not guaranteed to be nonzero does no good, but it's unnecessary here . |
- If your left (my denominator) integral does not vanish, everything is fine
- if it vanishes, one could bring your eq. in a similar form like mine (btw - what's that O(V_4) doing there - but anyway, it would vanish too)
In the latter case we could go and cancel the singularity from the polynomial fraction.
Kind regards,
Solkar |
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Barney
Anmeldedatum: 19.10.2008
Beiträge: 1538
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| Verfasst am: 11.07.2009, 07:38 Titel: |
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| Erik hat Folgendes geschrieben: |
The metric
\[ g = e^{2A(y)}g_{\mu\nu}(x) dx^\mu dx^\nu + g_{mn}(y)dy^n dy^m \]
is conformally equivalent to a metric of the form
\[ \bar g = g_{\mu\nu}(x)dx^\mu dx^\nu + \bar g_{mn}(y) dy^n dy^m. \]
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Hi Erik,
congratulation for this idea. That´s exactly the missing link to derive (3.5).
Now, we can investigate/think about further details/consequences of the D-dimensional gravitation theory, which is introduced by $\delta S = 0$ and S from (3.1). Another new topic is the physical meaning, i.e. implications of $S_4^{grav} = S_D^{grav}$.
BTW: A nice additional exercise is to derive eq (D.9) of Wald (could you give an exact reference/literature of this equation?) from the Besse equation (s. Wikipedia ). My first rough calculation shows, that both equations are identical modulo details, which are not important for our topic here.
br |
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Erik
Anmeldedatum: 28.03.2006
Beiträge: 565
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| Verfasst am: 11.07.2009, 13:18 Titel: |
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Thank you, Barney but it isn't really my idea. I think I just put everything that was already said
in this thread to the right and comprehensive order.
But now for some critical points of Solkars derivation leading to the answer of a question
regarding mine. First a minor point:
| Solkar hat Folgendes geschrieben: |
Pls kindly attend that the action integrals of Hamilton's Principle <![CDATA[http://en.wikipedia.org/wiki/Hamilton's_principle]]>(*) are meaningful in terms of stationary points on the Lagrangian function space, not because of their absolute value (and integrals are linear functionals).
$S_4^{grav} = S_D^{grav }$(VII.4)
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This eq. makes not much sense, from a pure mathematical point of view. S_4 is a functional
on the space of all 4-dimensional metrics, whereas S_D is a functional on the space of all
D-dimensional metrics. They cannot possibly be equal (as functionals, i.e give the same
value for every metric), unless D=4, which is the tautological case. (Note that S_D
explicitly depends on the XD metric g_mn.)
It is only after integrating out all the XD in S_D, (and getting rid of irrelevant
terms) that you can identify them. Please, look again at the paper by Randall and Sundrum.
They do it the same way: first substituting the metric and then integrating over the XD and
then calling the result the effective 4-dimensional action. So these steps should be reversed
in your derivation. The following is more important.
| Zitat: |
$\Rightarrow \frac{M_4^2}{M_D^{D-2}} = \frac{\int \frac{d^Dx}{{(2\pi)}^{D-4}} \sqrt{-g_D} \mathcal{R}_D}{\int d^4 x \sqrt{-g_4} \mathcal{R}_4}$(VII.6)
Now Fubini-Decomposition, replacing of $R_D$ with $R_4$ as shown at R&S eq(15) and applying the conformant re-scaling sampled here
$\Rightarrow \frac{M_4^2}{M_D^{D-2}} = \frac{\int d^4x \int \frac{d^{D-4}x}{{(2\pi)}^{D-4}}\sqrt{g_{D-4}} e^{2A} \sqrt{-g_4} \mathcal{R}_4} {\int d^4x \sqrt{-g_{4}}\mathcal{R}_4}$(VII.7)
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Apart from the criticism above the transition from VII.6 to VII.7 is clearly only valid for
constant A and conformally scalar-flat (i.e. scalar-flat after conformal transformation)
extra dimensions, or otherwise it contradicts the theorem cited above in my previous post.
(The one taken from Wald.)
But constant A is not in the sense of the rest of the paper by Giddings & Mangano, and
conformal-scalar-flat XDs are not required.
Together both points answer your question:
| Zitat: |
(btw - what's that O(V_4) doing there - but anyway, it would vanish too)
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I adressed this point in my post. It arises by integrating $ \sqrt{-g_4}R'(y) $ over y.
This gives the integral of a constant over the whole ordinary space time, resulting in
something proportional to V_4. And, you're right, it has to vanish, but you have to re-gauge the
lagrangian for this. This is an explicit step.
These additional terms $ \sqrt{-g_4}R'(y) $ in the S_D action are precisely the
reason why there is a $ \supset $-sign instead of an = in eq. (15) of the Randall Sundrum paper.
And they're missing in your derivation.
| Zitat: |
- If your left (my denominator) integral does not vanish, everything is fine
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Well, it does not vanish for every 4-dim. metric, so I can conclude that the constants
in front of the integrals are equal. S_4=0 does not cause trouble, since I don't divide by
S_4.
| Zitat: |
- if it vanishes, one could bring your eq. in a similar form like mine
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How? If it vanishes, it's 0=0. But fortunately this doesn't matter the slightest. |
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Solkar
Anmeldedatum: 29.05.2009
Beiträge: 293
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| Verfasst am: 11.07.2009, 15:15 Titel: |
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HI gentlemen!
| Barney hat Folgendes geschrieben: | | Erik hat Folgendes geschrieben: | The metric
\[ g = e^{2A(y)}g_{\mu\nu}(x) dx^\mu dx^\nu + g_{mn}(y)dy^n dy^m \]
is conformally equivalent to a metric of the form
\[ \bar g = g_{\mu\nu}(x)dx^\mu dx^\nu + \bar g_{mn}(y) dy^n dy^m. \]
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If one multiplies both sides of the upper eq with $e^{-2A(y)}$ the lower is yielded effortlessly.
That is what I used here.
| Barney hat Folgendes geschrieben: | | BTW: A nice additional exercise is to derive eq (D.9) of Wald (could you give an exact reference/literature of this equation?) from the Besse equation (s. Wikipedia ). |
That is a good idea, but I'd like to put this in a seperate thread; otherwise the readers might lose the connection to the main topic.
| Barney hat Folgendes geschrieben: | | My first rough calculation shows, that both equations are identical modulo details, which are not important for our topic here. br |
That's my impression as well and because we discussed Besse's formula again around this topic, we might indeed have two sides of the same medal.
| Erik hat Folgendes geschrieben: | These additional terms $ \sqrt{-g_4}R'(y) $ in the S_D action are precisely the
reason why there is a $ \supset $-sign instead of an = in eq. (15) of the Randall Sundrum paper.
And they're missing in your derivation. |
No I'm simply using a naming convention closer to that of G&M. That'S the reason why I added the "grav" index to the D-Dim gravitational action.
| Erik hat Folgendes geschrieben: | | How? If it vanishes, it's 0=0. |
Beforehand and by the same "trick" one always uses to get rid of common zeros, be them seperated by an equation sign or top and bottom a polynomial factorial:
One uses implications "=>" instead of equivalencies "<=>" .
Let $A_i(\mathbb{M})$ be a true predicate for all $m \epsilon M$, then $A_i(\mathbb{M}\setminus\{\aleph\})$ is also a true predicate. If one uses valid implications on $A_{\mu}(\mathbb{M}\setminus\{\aleph\})$ subsequently following and finds that at a certain point $A_j(\aleph)$ is also true (eg, because a polynom has become invariant of one former term) one can establish $A_j(\mathbb{M})$ and carry on.
That is the basic idea behind canceling removable singularities from a polynomial fraction.
And even if one puts it verbally, like you, Erik, did
| Erik hat Folgendes geschrieben: | | In order for this to hold for every metric[...] |
the very concept of getting rid of common, maybe "pathological", terms is still the same.
---
I'd be most willing to discussing this (most of all because singularities are a major point in complex analysis (Funktionentheorie) and that is my "pet" subject) and also participate in a discussion about Wald's/Besse's theorems,
but I'd like to suggest that we put this into a seperate thread.
@moderators: I'd like to propose a "Mathematical" Sub-Forum btw.
===
For the time being I think we're at least in agreement that
- there is a way to get to G&M (3.5)
- Randall/Sundrum do have to do with it
- R-singularities can be removed one way or another.
That's imo fair enough for being able to proceed to G&M ch. 3.2.:
---
G&M eq(3.15) is said to be deduced from a 1963 paper of F.R. Tangherlini; I'll attend a scientific library on monday, so I might ge ta chance to get a look at it
---
That leaves us at G&M ch. 3.2.2
Best regards,
Solkar |
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Erik
Anmeldedatum: 28.03.2006
Beiträge: 565
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| Verfasst am: 11.07.2009, 23:08 Titel: |
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| Solkar hat Folgendes geschrieben: | HI gentlemen!
| Barney hat Folgendes geschrieben: | | Erik hat Folgendes geschrieben: | The metric
\[ g = e^{2A(y)}g_{\mu\nu}(x) dx^\mu dx^\nu + g_{mn}(y)dy^n dy^m \]
is conformally equivalent to a metric of the form
\[ \bar g = g_{\mu\nu}(x)dx^\mu dx^\nu + \bar g_{mn}(y) dy^n dy^m. \]
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If one multiplies both sides of the upper eq with $e^{-2A(y)}$ the lower is yielded effortlessly.
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Like I said immediately after the quoted passage: "the conformal factor being $ e^A $."
Meaning $ (dx,dy)\mapsto e^A (dx,dy) $ and consequently $ g = e^{2A}\bar g $. Getting from one
metric to the other was not the point here. The point was that R is of much an easier form when calculated
from the 2nd metric.
| Zitat: |
That is what I used here.
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From that post it isn't clear how the D dimensional R relates to the 4-dimensional one
calculated from $ g_{\mu\nu}(x) $ alone. The relation implicitly used in your
derivation by getting from VII.6 to VII.7 is wrong (or requires constant A and a special
geometry of the XD).
| Zitat: |
| Erik hat Folgendes geschrieben: | These additional terms $ \sqrt{-g_4}R'(y) $ in the S_D action are precisely the
reason why there is a $ \supset $-sign instead of an = in eq. (15) of the Randall Sundrum paper.
And they're missing in your derivation. |
No I'm simply using a naming convention closer to that of G&M. That'S the reason why I added the "grav" index to the D-Dim gravitational action.
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Sorry, I thought it was clear that my disagreement had absolutely nothing to do with naming
conventions. You fail to give the right relation between D dimensional R and R_4.
(Why do you think adding the index "grav" anywhere is of any importance to my objection?
Do you think the "missing terms" refer to the matter part of the action? That's not the case.)
| Zitat: |
| Erik hat Folgendes geschrieben: | | How? If it vanishes, it's 0=0. |
Beforehand and by the same "trick" one always uses to get rid of common zeros, be them seperated by an equation sign or top and bottom a polynomial factorial:
One uses implications "=>" instead of equivalencies "<=>" .
Let $A_i(\mathbb{M})$ be a true predicate for all $m \epsilon M$, then $A_i(\mathbb{M}\setminus\{\aleph\})$ is also a true predicate. If one uses valid implications on $A_{\mu}(\mathbb{M}\setminus\{\aleph\})$ subsequently following and finds that at a certain point $A_j(\aleph)$ is also true (eg, because a polynom has become invariant of one former term) one can establish $A_j(\mathbb{M})$ and carry on.
That is the basic idea behind canceling removable singularities from a polynomial fraction.
And even if one puts it verbally, like you, Erik, did
| Erik hat Folgendes geschrieben: | | In order for this to hold for every metric[...] |
the very concept of getting rid of common, maybe "pathological", terms is still the same.
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Hm, your replies are becoming more and more obscure to me. I have no idea what you are trying to say
here, but I'm suspecting that you misunderstood something. The point of my argument containing the
quoted phrase was not to get rid of any terms or zeros.
| Zitat: |
I'd be most willing to discussing this (most of all because singularities are a major point in complex analysis (Funktionentheorie) and that is my "pet" subject) and also participate in a discussion about Wald's/Besse's theorems,
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I don't think this has anything to do with complex analysis or singularities.
| Zitat: |
For the time being I think we're at least in agreement that
- there is a way to get to G&M (3.5)
- Randall/Sundrum do have to do with it
- R-singularities can be removed one way or another.
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What do you mean by R-singularities? |
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Solkar
Anmeldedatum: 29.05.2009
Beiträge: 293
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| Verfasst am: 12.07.2009, 02:09 Titel: |
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Erik,
| Erik hat Folgendes geschrieben: | | Why do you think adding the index "grav" anywhere is of any importance to my objection? |
there's no season for you to become upset; especially not if
| Solkar hat Folgendes geschrieben: | | I'd be most willing to discussing this (most of all because singularities are a major point in complex analysis (Funktionentheorie) and that is my "pet" subject) and also participate in a discussion about Wald's/Besse's theorems, |
along with the posting you become invited to discuss higher analysis with somebody.
Had I been too subtle on the latter?
While talking about
| Erik hat Folgendes geschrieben: | | Hm, your replies are becoming more and more obscure to me. |
manners:
what is also a little, well - "miraculous" (that's a nice term, wouldn't you agree?) is how you despite this
| Zitat: | | I have no idea what you are trying to say here, |
arrive here
| Zitat: | | but I'm suspecting that you misunderstood something. |
But anyway - I was talking about polynomial fractions and equations - you were disputing that common zeros could be canceled and I reiterated the basic concept of it for you.
Is that really difficult for you?
Or were you just trying to "make a joke"?
I guess it's the latter, isn't it?
Kind regards,
Solkar |
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Barney
Anmeldedatum: 19.10.2008
Beiträge: 1538
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| Verfasst am: 12.07.2009, 07:59 Titel: |
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| Erik hat Folgendes geschrieben: |
This eq. makes not much sense, from a pure mathematical point of view. S_4 is a functional
on the space of all 4-dimensional metrics, whereas S_D is a functional on the space of all
D-dimensional metrics. They cannot possibly be equal (as functionals, i.e give the same
value for every metric), unless D=4, which is the tautological case. (Note that S_D
explicitly depends on the XD metric g_mn.)
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Hi Erik and Solkar,
in my very personal opinion the equation $S_4^{grav} = S_D^{grav}$ makes not too much sense at all. Of course, it is the main physical hypothesis of the whole paper and it seems to be a, respectively the core hypothesis of string theory. But I don´t think that nature is such simple. Now, I could leave the whole topic and do further studies of the beloved Heim theory, but on the other hand, this way may be only a holy dream....
Therefore my personal future currently isn´t predestined, but this is another well known philosphical topic.
Kind regards and have a healthy sunday without struggles about untested hypotheses. |
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Solkar
Anmeldedatum: 29.05.2009
Beiträge: 293
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| Verfasst am: 12.07.2009, 11:20 Titel: |
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Hi Barney,
| Barney hat Folgendes geschrieben: | | in my very personal opinion the equation $S_4^{grav} = S_D^{grav}$ makes not too much sense at all. Of course, it is the main physical hypothesis of the whole paper and it seems to be a, respectively the core hypothesis of string theory. But I don´t think that nature is such simple. |
I think nature is even "simpler" than ST implies - in terms of the basic concepts, not in terms of its mathematical formulation. But these are topics of core beliefs, hardly to substantiate without falsifiable thesis, so this
| Barney hat Folgendes geschrieben: | | [...] struggles about untested hypotheses. |
is imho a good point.
Personally speaking, I'd like to see a clear falsification criteria of the whole ST. My impression is that it all started as a quest for Planck scale, and the harder it was to get that out, the more complicated theories were mounted up. I read the first book about ST more than ten years ago. Since that time people received professorship for working on it, and to my great amazement after all that time ST obviously has still not been sufficiently tested.
A pleasant sunday to you!
Kind regards,
Solkar
P.S: I would appreciate it a lot if you continue contributing to this thread |
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Erik
Anmeldedatum: 28.03.2006
Beiträge: 565
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| Verfasst am: 12.07.2009, 11:29 Titel: |
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| Solkar hat Folgendes geschrieben: |
| Erik hat Folgendes geschrieben: | Why do you think adding the index "grav" anywhere is of any importance to my
objection? Do you think the "missing terms" refer to the matter part of the action?
That's not the case.)
[quote completed]
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there's no season for you to become upset; especially not if
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??? You seem to have taken something the wrong way. I'm not upset the slightest bit. I was
just trying to interpret your answer to me and correct a possible misinterpretation.
| Zitat: |
| Solkar hat Folgendes geschrieben: | | I'd be most willing to discussing this (most of all because singularities are a major point in complex analysis (Funktionentheorie) and that is my "pet" subject) and also participate in a discussion about Wald's/Besse's theorems, |
along with the posting you become invited to discuss higher analysis with somebody.
Had I been too subtle on the latter?
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I already started a discussion about the theorem cited from Wald and how I think your
derivation is in conflict with it. But you don't seem to be very interested (ignored, as
ususal, most of what I said on this.) On the other hand I don't think that this has anything
to do with complex analysis.
| Zitat: |
While talking about
| Erik hat Folgendes geschrieben: | | Hm, your replies are becoming more and more obscure to me. |
manners:
what is also a little, well - "miraculous" (that's a nice term, wouldn't you agree?)
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Oh, the word "obscure" was offending you? That was not my intention. I think it
just means "unclear". (And BTW, your second reply to me in this discussion was alleging a
"lack of logic", so you better be not too sensitive on this topic. I surely am not.)
| Zitat: |
is how you despite this
| Zitat: | | I have no idea what you are trying to say here, |
arrive here
| Zitat: | | but I'm suspecting that you misunderstood something. |
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That I was trying to explain: You are talking about getting rid of terms and zeros while
quoting a phrase of mine out of a completely different context. So I was suspecting that you
misunderstood what I was trying to say with that phrase. That's all.
| Zitat: |
But anyway - I was talking about polynomial fractions and equations - you were disputing that common zeros could be canceled and I reiterated the basic concept of it for you.
Is that really difficult for you?
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When did I talk about canceling zeros? (That was you I think.) I was talking more or less
about some trivial kind of equating coefficients. The zeros of the involved functionals
don't interest me much.
| Zitat: |
Or were you just trying to "make a joke"?
I guess it's the latter, isn't it?
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Calm down and guess again. |
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Eric
Anmeldedatum: 25.10.2009
Beiträge: 3
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| Verfasst am: 25.10.2009, 23:52 Titel: Could there be a serious error in M&G calculations here. |
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I hope the following can be seriously considered:
Does the 5dimensional formula M&G relied on (as shown be p.26), for warped accretion calculations in the Bondi phase, equation (4.40) of p.24, correctly involve, for its derivation, the Randall/Sundrum specific formulae for this warped context: equations(3.23) to (3.26) of p.13?
nb My German is not good; I have been unsuccessful getting detailed arguments on this issue considered with English language based physics forums. |
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Barney
Anmeldedatum: 19.10.2008
Beiträge: 1538
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| Verfasst am: 26.10.2009, 09:55 Titel: |
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Hi Eric,
first of all a friendly welcome to the AC-Forum. It seems, that you want to discuss more or less some implications of the Randall-Sundrum model. Therefore your question is more or less off topic. Nevertheless you can read here, very shortly, my first reaction regarding the Randall-Sundrum model.
br |
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Solkar
Anmeldedatum: 29.05.2009
Beiträge: 293
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| Verfasst am: 26.10.2009, 12:09 Titel: |
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Hi Eric!
It's good you joined us here.
Here's not an analytical, let alone a numerical, review, but possibly an ansatz:
[GM08] p. 26, ch. 4.4, first paragraph
| Giddings & Mangano hat Folgendes geschrieben: | | In this case, we have $D$-dimensional evolution up to capture radius $R_D$, then a warped evolution up to $R_C$, then four-dimensional evolution from then on. |
So it appears that the authors don't have to deal with warping yet when they calculate the time to arrive at $R_D$ (same page and chapter, middle of third paragraph),
| Giddings & Mangano hat Folgendes geschrieben: | | If, in line with our discussion of scales, we take $R_D\approx 0.02\ mm$, the evolution time up to this radius follows from (4.40) |
whereas the value of $R_D$ was deduced above (4.51) deploying (3.26) and misc.
If that doesn't appear to you overly conclusive yet - well, It doesn't even appear so to me...
But, as I said, that was at best an ansatz; maybe we can refine that.
With kind regards,
Solkar
Refs (BibTeX):
=============
[GM08]
@article{Giddings:2008gr,
author = "Giddings, Steven B. and Mangano, Michelangelo L.",
title = "{Astrophysical implications of hypothetical stable TeV-
scale black holes}",
year = "2008",
url = "http://arxiv.org/abs/0806.3381v2",
journal = "Phys. Rev.",
volume = "D78",
pages = "035009",
eprint = "0806.3381",
archivePrefix = "arXiv",
primaryClass = "hep-ph",
doi = "10.1103/PhysRevD.78.035009",
SLACcitation = "%%CITATION = 0806.3381;%%"
} |
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Eric
Anmeldedatum: 25.10.2009
Beiträge: 3
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| Verfasst am: 26.10.2009, 18:11 Titel: |
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Quite right, Solkar and hello.
I don't know how I missed that. But how can 4.40 be used for pre Bondi? This has to be a mistake or assumes pre Bondi is of negligible duration; but there is no R-S specific pre Bondi formula, which itself (Rem 4.10) there is only one of and it doesn't include the identifying k^ (3.24-3.25) for the R-S scenario.
Even if 4.40 is for R-S specifically, I would predict that it is not the correct one for the unwarped domain of the warped compacitfication of R-S, as it doesn't relate to the warped range eq24 to 3.25 (where RD< r< L). The latter is where the warped gravitation force formulae is established.
So then the formulae for warped Bondi accretion above RD is not specified. Seemingly though this would have to be the only 5dim one, eq4.40 again.
All this leads me to suggest 4.40 is not warp speciic as it should be. But the question remains the derivation of it. |
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Eric
Anmeldedatum: 25.10.2009
Beiträge: 3
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| Verfasst am: 27.10.2009, 03:39 Titel: |
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I have now seen that in the case of warped Bondi accretion, p.26 deals with this anyway in a conservative fashion by assuming the Bondi radius is equal to the minimum classical scale Rc throughout the warped phase (the Bondi radius couldn't be greater than this because of much lower 4d gravity)*. This is because the gravitational force formulae are used to derive the Schwarzschild radius (except in case of R-S) and thereby the Bondi radius.
I seems that M&G don't want to get into involved calculation that rely on the R-S formula giving the D=5 black hole gravitational force. It maybe, as M&G seem to assume, that below the warped scale the alternative ADD model works out in the same way as R-S, but I haven't seen confirmation of that and the models are quite different : ADD doesn't rely on D branes.
*This overcomes a problem I see in Plaga's paper where Bondi radius reaches 4mm. However I calculated that the results would still be catastrophic at 4 or so orders of magnitude lower luminosities. Plaga didn't seem to go along with this when I mentioned it to him - I don't think he got my point. |
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Solkar
Anmeldedatum: 29.05.2009
Beiträge: 293
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| Verfasst am: 28.10.2009, 07:23 Titel: |
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| Eric hat Folgendes geschrieben: | | This is because the gravitational force formulae are used to derive the Schwarzschild radius |
There's no reference for [GM08] eq(3.15), so unfortunately some "guessing work" is needed:
[GM08] refers to [MP86] (their [29]) in a sideline below their eq. (3.18) regarding Kerr-Solutions;
[MP86] refers to [Tan63] where there are some equations "similar" to [GM08] eq(3.15) - eq(3.18) at pp. 641 - 642; I don't get the exact match yet, but I'm working on that.
| Eric hat Folgendes geschrieben: | | (except in case of R-S) and thereby the Bondi radius. |
The generalized Bondi radius ("BR") is defined in [GM08] eq. (A.18) in terms of (amongst others) $c_s$, which is related to grav. fields $\Phi$ by eq (A.9). The fields are, of course, deduced from the metric.
| Eric hat Folgendes geschrieben: | | I seems that M&G don't want to get into involved calculation that rely on the R-S formula giving the D=5 black hole gravitational force. It maybe, as M&G seem to assume, that below the warped scale the alternative ADD model works out in the same way as R-S, but I haven't seen confirmation of that and the models are quite different : ADD doesn't rely on D branes. |
I understand you've already spent some work on that; could you provide some references, pls?
There's [RS99] and here's a list of publications of the "ADD" authors on arXiv
| Eric hat Folgendes geschrieben: | | This overcomes a problem I see in Plaga's paper where Bondi radius reaches 4mm. |
For the purpose of discussing Dr.Plaga's most recent paper I had blogged here, I'd most appreciate if you added your findings; There were also some German remarks published in this forum recently which I intend to discuss in that blog asap
C u,
Solkar
Refs (BibTeX)
=============
[MP86]
@article{Myers:1986un,
author = "Myers, Robert C. and Perry, M. J.",
title = "{Black Holes in Higher Dimensional Space-Times}",
journal = "Ann. Phys.",
volume = "172",
year = "1986",
pages = "304",
doi = "10.1016/0003-4916(86)90186-7",
SLACcitation = "%%CITATION = APNYA,172,304;%%"
}
[Tan63]
@article{Tangherlini:1963bw,
author = "Tangherlini, F. R.",
title = "{Schwarzschild field in n dimensions and the dimensionality
of space problem}",
journal = "Nuovo Cim.",
volume = "27",
year = "1963",
pages = "636-651",
doi = "10.1007/BF02784569",
SLACcitation = "%%CITATION = NUCIA,27,636;%%"
}
[RS99]
@article{Randall:1999ee,
author = "Randall, Lisa and Sundrum, Raman",
title = "{A large mass hierarchy from a small extra dimension}",
url = "http://arxiv.org/abs/hep-ph/9905221v1",
journal = "Phys. Rev. Lett.",
volume = "83",
year = "1999",
pages = "3370-3373",
eprint = "hep-ph/9905221",
archivePrefix = "arXiv",
doi = "10.1103/PhysRevLett.83.3370",
SLACcitation = "%%CITATION = HEP-PH/9905221;%%"
} |
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