cows

Anyways looking for some feedback on my latest ramblings

Ok this did not take too long

Maldacena seems to confirm as much by looking at four dimensions and doing a different wrapping, getting (2.6.1) which bears a different form.

Ok it seems this is true as I had suggested way before looking at Maldecena.

Can someone comment on this?

It does seem though that the entropy is not going to be unique but would depend on the wrapping mechanism.

I think I can reproduce this independently now ( ok fine because I have seen how it is done now)

@MitchellPorter I think I cracked the code! (2.38) and (2.39) in Maldacena derive (22.138) in Zwiebach. This is done through the area law.

not as bad

Oh! now ramond - ramond kicks in

2.5.1. of Maldecena seems to show the mechanism for the construction of the extremal black holes in 5 dimensions. This might be a good starting point

.. it seems. Let me check

D branes must contort

Yes he does on page 5

Let me check if Maldacena says as much

charge becomes mass

Maybe let us start with Kerr-Newmann and derive the extremal conditions

Someone please construct this

It seems the first step is to construct an extremal black hole.

BTW , I need someone to check me as I ramble on

We are doing stuff in 5 dimensions basically it seems 5 curled

one is working in Type II B string theory at low energy it seems

Two things seem to be evident

Ok let me still do some talking and open reasoning along the way.

This might take a few days

@MitchellPorter thank you I am taking a look at it now

I have now edited the question and removed the mention of high school-level math. I also just asked the question directly about, as in what is a black hole microstate and how is counting done. Perhaps some good nice answers might come up

@Ghoster At any rate, what do you make of my ramblings thus far?

@Ghoster, I am now ok with $ln P(N;b,f) ~ 2 \pi \sqrt{N/6 (b + f/2)}$ but not (22.142) I feel like this is the final step

So I want to know a bit more about the formula: $ S = 2 \pi \sqrt{N Q_1 Q_5}$ .. . (22.138) Zwiebach. Also I want to guess that the charges could be different here based on how we do the wrapping of branes.

At any rate one can extend this Kalb- Ramond thing to Ramond -Ramond or some such thing for branes and then use some voodoo (dimensional ) to get an effective maxwell field. So one can get charges this way. ok

$\frac{1}{k^2} = \frac{ \partial H^{\mu \nu \rho}}{dx^{\rho}} = j^{\mu \nu}$ one can compute vector charges and so on later

So I have read this now. Let me try to organize my thoughts first if this is even possible. Ok. It turns out that the framework where this is easiest to do is supergravity at least according to the text. Something like some approximation of Type IIB. ok sure. The specific construction of the extremal black hole in 5d is not quite discussed but ok. The expression for the entropy has charges. So I scribbled some analogues of standard things with gauge fields -- and field strengths, then upgraded to the Kalb-Ramond fields which I have asked about before on this site.

It seems his name is Zwiebach. I get the spelling wrong every time too.

@Ghoster Oh! I had no idea Zweibach's text had this too. We used the first part of this text and other texts for our graduate string theory class. There is a second semester of the string course coming up in Spring I believe. Maybe we will also cover this then. Ok, I have just now opened that page in the text. I think I will aim at reading and doing the exercises in chapter 22 starting right this minute.

Ok we can get technical now.

ok so how are these things calculated without appeal to ads/cft?

Ok, so it would seem to me, continuing down this rabbit hole that one computes the total energy of the system, then computes the "combinations" that give the total energy in the stringy system. One needs a partition function to begin.

Basically, you inject a known amount of energy in the system, and then count.

@Ghoster Ok, let's just start by saying a black hole is a collection of strings that are excited and doing their thing. We can get more technical but for the purposes of understanding let's start soft. So sitting here in bed and drinking a coffee, I am thinking to myself you need a number for the number of strings to form said ball being called a black hole, then one looks at the combinations and arrangements of energy packets amongst the strings. Again, omitting technical details and all for now. Please check the concept and let me know if I'm getting warmer.

It might also be helpful to even learn what a quantum state of a black hole is

@Ghoster, I don't know. I always feel like there could be a high-school-level explanation for every concept, math and all included or at least something where the steps are shown/ worked out.

@SBrian Yes. I think this would be helpful too. The blackhole itself is different from the spacetime around the black hole.

starting chapter 3 now.

Reading chapter 2. Learning notation and definitions

Let us continue this discussion in chat.

Thank heavens for google. I am now looking up a lot of new math vocabulary while still just reading chapter 1.

I'll be reading the first chapter today.

ok, I just got the book. I have a copy with me now.

Yes, thank you. I will be ordering the book today. There's quite a bit i need to learn.