The relationship between geometry and energy for gravitational waves

By continuing the last post, we will talk a little about the sources of gravitational waves. Of course that the subject can be found in many other places, for example the wikipedia site. However, my hope is to add something besides the content at Wikipedia.

Well, we know that gravitational waves are predicted by the Einstein's general relativity. The main equation of the theory is called the "Einstein's equation" which is a tensor equation. We can see it below.

R_μν -g_μνR/2 = 8πGT_μν/3

Here, the R_μν and R terms are elements of geometry and the T_μν term represents elements of density of mass and energy; g_μν is the metric of space and the other terms are constants values.

As we can note we have geometry elements on left-side and matter elements on right-side. This equation shows a way of interacting the geometry of the universe (of a piece of it) and the distribution of mass (or matter, or energy) on the space-time. Thus, we will have just a space-time completely smooth if there is no matter in all space-time. From the moment that we have the presence of a small density of matter, the geometry of space-time is not smooth any more. What we need know more is that all space time geometry is defined by the metric.

Now if we want gravitational waves, which are deformations on the gravitational field (represented by the metric) we need to insert something else in the metric. We need just insert a small perturbation on it. Thus mathematically speaking, gravitational waves are a kind of perturbations on the space-time metric. By inserting  a perturbative term in the metric and by solving the Einstein equation it's possible to visualize gravitational waves.


So in order to visualize the solution for gravitational waves from the a certain massive body, we must insert in the Einstein equation the elements of geometry of the region where the body is localized and its distribution of matter (or energy). Some examples of possible sources of gravitational waves are black hole, extremely massive stars, and the main one, an inflationary period which took place in the first stages of our universe. I say main because gravitational waves that were generated in this special period can carry very important information about the first minutes or even seconds of the universe.

Two problems of exchange of knowledge

The sharing of knowledge is an important step which must be done if we wish that the world be more and more sociable. In this mechanism we have the exchange of knowledge between Professor  students in the University as well as between the "scientists" (Professor and students) and the society in general.
Of course, there are problems in all countries about it, even that it be different one of another.

I post here two little articles about this subject and I hope that they can be usefull for someone. One of them is about the exchange of knowledge between the scientists and the society and the another one is about the transfer of knowledge from Professor of physics to students of physics.

The first article, named  How to not Teach Physics shows the exchange that I have cited first, and the second exchange being discussed in the article named Social Media for Scientists Part 1: It's Our Job.

The link for the articles can be seen below:  

http://blogs.scientificamerican.com/science-sushi/2011/09/27/social-media-for-scientists-part-1-its-our-job/

http://dissidentvoice.org/2013/01/how-to-not-teach-physics/

Just as a comment, here in Brazil we have both problems deeply. The society in general does not care if you collide two protons at a accelerator or if you is capable of moving a metal arm with your mind. Of course, the magazines most popular are not doing their job right, what makes the situation worse.

By the other hand, we have good students of science in general, particulary in physics, but unfortunately they are not valued neither by companies nor government agencies.