Perfect fluid energymomentum tensor in special relativity. Theoretical physicists prefer a di erent formulation, which dictates the general form of equations in theoretical mechanics. At this point if we were going to discuss general relativity we would have to learn what a manifold 16. The essential mathematics of general relativity is di. Lecture notes on general relativity matthias blau universitat bern. This is a symmetric tensor that defines the distance between two neighboring. The metric or inverse metric tensor allow all of these tensors to be transformed into each other. Notes from professor leonard susskind video lectures publicly available on youtube. Simply put, a tensor is a mathematical construction that eats a bunch of vectors, and spits out a scalar. It may loosely be thought of as a generalization of the gravitational potential of newtonian gravitation. Introduction to tensor calculus for general relativity.
Introduction to general relativity and cosmology living script astro 405505 isu fall 2004 dirk putzfeld iowa state university 2004 last update. It is called the metric tensor because it defines the way length is measured. For your convenience, i present to you, in a single paragraph, the essence of tensor analysis. Metric tensor in special and general relativity physics. Returning to equation 22, we see why we must distinguish vectors.
The most important tensor in gr is the metric g, a generalization to arbitrary coor dinates and geometries of the minkowski metric. In this formulation the focus is on the experiments. In general relativity, the metric tensor in this context often abbreviated to simply the metric is the fundamental object of study. A key feature of this equation of motion is that it does not involve the. Im having trouble understanding the metric tensor in general relativity. Einsteins road to general relativity began in november 1907. General coordinate transformations in minkowski space i. The blog contains answers to his exercises, commentaries, questions and more.
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