Saturday, July 19, 2014

Numerical Relativity: Black Holes and Gravity - Part 1

Before getting into the gr-qc publications, I would like to give you some information on this field of study. I recommend knowledge of special relativity, but it is not required. These posts will begin at a low level and become a bit more difficult as we go on. If you are already well acquainted with the concepts and the jargon, you are welcomed to skip them and start at the first gr-qc post.

What is Gravity and How Do We Think about It?


Gravity is one of the four fundamental forces. In fact, it is the weakest one! However, an advantage of gravity is that it is a long-range force, which is useful to us when trying to measure interactions. Gravity is the force behind the big bang, black holes, and stars. Gravitational physics is of extreme importance is both large and small scales - from cosmology to quantum physics.

A look into Newtonian gravity will give you the following equation:
$$  F_{grav} =  \frac{Gm_1m_2}{r_{1,2}^2} $$
which says that the force between two bodies is related to their mass and distance. However, the problem with Newton's view is that the force is instantaneous. This is not allowed, as shown in special relativity where nothing can travel faster than the speed of light. Therefore, we say that Newtonian gravity is an approximation only. 

We first think of gravity as an accelerating force. For example, in classical physics we are introduced to objects falling from a certain height of being thrown upward at a certain angle. However, when we are exposed to more advanced topics, we begin thinking of gravity as a field with stored energy. However, we can all agree that gravity is geometry. We first study gravity using Euclidean geometry and then go on to learn about non-Euclidean geometry, such as that of the surface of a two dimensional sphere of a radius R. We could go on to talk about different coordinates and invariance, but what we have talked about suffices for now. 
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