Sad Ending
That’s it. The class is over… I have to admit that I’m pretty sad to see the end of it, although I’m very very tired. It was such a great group. (I’ll be toasting the end of it all with some of the splendid stuff to the right.)
Recall that we stepped away from black holes. After a look at cosmology for some lectures, where we understood the role of four crucial components in determining a universe’s properties (curvature, matter, radiation, and vacuum energy) we dove back into formalism for a short while (one lecture) to develop a little more the tools we needed to properly under stand how to formulate Einstein’s field equations.
It did not take long… You need only the idea that it makes sense to formulate everything in terms of objects that allow you to express the full sense of an equation in any coordinate system you care to write. Once that is done (the objects are called tensors, and the idea and how they work is pretty simple to get to grips with) the key to formulating the field equations of gravity is to have a look at the structure of other familiar systems. The field equations of electromagnetism (Maxwell’s equations) and the field equations for Newton’s formulation of gravity give the required clues. A rummage around the geometry to find the appropriate object to express the physics in terms of uncovers the Riemann tensor and its cousins (“contractions” to get Ricci and so forth), and you’re almost there. A step back to learn how to package energy […] Click to continue reading this post