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.

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!

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...

Spacetime geodesics (I).

Math, again, people!

A couple of posts ago I introduced myself to geodesics as free fall trajectories in curved spacetime. The problem with this description -one of them- is it's saying not enough. What I've learned since then about geodesics it's still not enough, but it's a step forward, so better than nothing.

This post was intended to solve geodesic equation for an easy case and show that spacetime nature depends on 4 coordinates -3 in space and 1 in time. The problem is the answer is not as straightforward as I expected. Let's see it anyway.

A geodesic is a curve. And like any curve, it can be described mathematically. General, index form is:

Leonard Susskind's GR lectures at Stanford.

I discovered Leonard Susskind because of the book "The black hole war". It was interesting and funny and the fact I was not able to grasp the last part of it -that holographic metaphore is disturbing-, didn't make me dislike it at all. I started to look at physicists more like human beings thanks to it. And that's saying a lot.

Before that, my only contact with physicists were close related hate-filled-relationships due to the fact engineering physics in Spain -the time I studied it, at least- were intended more to make an IQ selection than teaching actual interesting physics. I can blame no one for that. It's a consequence -one of the bad ones- of having a public university model. Good ones outnumbered bad ones, by the way. In the future, who knows.

 

Leonard Susskind a couple of years ago. From Stanford web.