Coursera's introduction into General Relativity

I was lured recently to a Coursera's course in General Relativity. It is a course hosted by Emil Akhmedov, professor in the Higher School of Economics.

Do you think too coursera's logo looks like some kind of brand for a dark society?

Not gonna lie, it's not easy but at least it's formal enough to make me re-learn tensor handling in a way Susskind can not. Not his goal anyway. Here is the web in case you want to check it out.

The speed of gravity

The internet is full of cats and porn. No breaking news, here. There are a lot of other places with interesting information, though. One of them is the askscience of reddit. If you follow the link, you'll find this one too.

The question stated is: if gravity is transferred at $c$ (speed of light), and Sun is 8 minutes away at $c$, regarding the fact the Sun moves, does it mean Earth is attracted to the position the Sun had 8 minutes ago?

Video is from a guy named DjSadhu. Music is cool, if you ask me.

Spacetime as a consequence of something else: ER=EPR.

There's so much I don't know about GR that talking about interpretations and physics trends is a dangerous matter, specially if my words are intended to be, you know, taken seriously. That's the reason I try to focus in learning instead of trying to develop things on my own. And I don't always succeed anyway, so look at that.

Nevertheless sometimes comes the time when you find something interesting and you have to share it and... Well, hell, this is my blog, right?

I have found recently the ER=EPR conjecture and I have tried to learn a bit about it. Shall we talk about it a little? I'll go on with Schwarzschild metric inside the Earth a little bit later. :)

Maxima ctensor overview

I have installed Maxima (finally) and I have been playing with it a little. First part of the post is about a general explanation about what Maxima's ctensor can and can't do. Second and third part will try to explain functionality with a couple of easy examples. I have not tried neither itensor nor atensor; as I stated in the past post, their functionality is not what I need for now.
So far, and summarizing, I must admit Maxima falls short for my intentions. Truth is it's a good tool anyway and it should be easy to adapt to what I want when I had the time to go for it.

Coming back ASAP

Sorry again. A couple of months have passed and I haven't find the time to continue with the posting. I should continue ASAP. I left the work at analyzing Maxima and Cadabra, which I should do in the next days, while I prepare my TOEIC exam -lot of work to do as you can see by my english level.

After that, truth is I don't have a clear idea of what to do next. I had a couple of posts ready about Earth nucleus age, and stuff like that but I'm not sure what should come next. Anyway, I should continue, so in a couple of days a new post will appear, but be patient please.

It's just things are not easy everytime :)

Open Source Computer Algebra Systems.

So, I started to look for computer help. As an open source freak, I have found two different packages available: Maxima and Cadabra. This post is about impressions on both of them. Not sure yet what I am going to use yet, but my hopes go to Maxima in a first approach.

Schwarzschild metric (V).

Did you really think we were done with Schwarzschild metric? We have finally found that...
\begin{equation}
ds^2= \left ( 1- \frac{2GM}{c^2r}\right )c^2dt^2- \frac{dr^2}{\left( 1- \frac{2GM}{c^2r}\right)}-r^2(d\theta^2+sin^2\theta d\varphi^2)
\end{equation}
... so... Good for us.

But what does that mean? Why is it important? Why is it useful?

Schwarzschild metric (IV)

This Schwarzchild Schwarzschild topic is getting out of hand!

Just two more posts. In this one we are going to find the final form of the metric. Next one is about interpretations, conclusions and such, which turns out is a lot more faster than deriving the metric itself...

So, here we go again... Math ahead!

Schwarzschild metric (III): the search for simplification

Stubborn as I am, I'm not going to continue with the demonstration demostration until I completely understand why $C=D=1$. I'm not saying it's wrong. Just saying I don't understand why it's right... Yet.
Spoiler: I have found a way of understanding it. Not sure is correct, but it's good for me at the moment. Yes. I do believe too that I have overthought this too much.

Betrand Russell advises.

It really has not much to do with GR, but in the moment I saw the video, I knew I had to post it.

Schwarzschild metric (II)

Are you ready?
We were supposed to end up with the demonstration, but it actually is pretty damn long, so in this post I'm going to just obtain the equations as functions of A, B, C and D. And I'll let the final steps of the demonstration for the next post. So two points already pendant:

1. Why metric tensor has only diagonal components? That is, why there are no cross-terms?
2. Applying $g_{\mu\nu}$ into the $R_{\mu\nu}$ equation.

Warning! Math ahead!

New look!

I'm finishing Schwarzschild post II: the Schwarzs strikes back. For the moment, as you can see, several look changes have been made to the blog. For the sake of clarity.

Maybe I add several changes more in the future. Maybe the font is a little bit small...

Edit: It turns out Mathjax doesn't work well with my android phone... Working on it! :)

Edit2 (05/16/16): It turns out I'm a moron and I didn't activate the custom layout in mobile needed for Mathjax to perform its magic. Several issues regarding line breaking in formulae still remain, so I suggest to use your mobile in landscape mode to fully enjoy the math for now :)

Schwarzschild metric (I)

Maybe I should start explaining what a metric is. Or curvature. Or the energy-stress tensor...

Nahhh... :)

Let's run before walk with an example. It's funnier this way.

Legend says Karl Schwarzschild was a german artillery officer during WWI, but the truth is he was a physicist and astronomer before that. He died several months after finding the first analytical solution to EFE's, of an illness called Pemphigus (click at your own risk). You have read right: Schwarzchild did find an analytical solution to Einstein Field Equations. Exactly. Analytically. Manly.

Truth be said, he did it for the "simplified" case of a spherical static object, but it's a good aproximation, specially for people like me who need to learn. Are you ready? I prevent you I have (finally) learned how to use latex in blogger...

Coming back soon!

Two years and a half. 

Two years. And. A. Half.

Lot of things have happened since the last post. Long story short, I have a little bit of free time again, so I'm preparing new posts in the point where I left.

Next stop, Schwartzschild metric.

See you soon!