Introduction To Mathematics Of General Relativity
The mathematics of general relativity is very complex. In Newton's theories of motions, an object's mass and length remain constant as it changes speed, and the rate of passage of time also remains unchanged. As a result, many problems in Newtonian mechanics can be solved with algebra alone. In relativity, on the other hand, mass, length, and the passage of time all change as an object's speed approaches the speed of light. The additional variables greatly complicate calculations of an object's motion. As a result, relativity requires the use of vectors, tensors, pseudotensors, curvilinear coordinates and many other complicated mathematical concepts.
All the mathematics discussed in this article were known before Einstein's general theory of relativity.
For an introduction based on the specific physical example of particles orbiting a large mass in circular orbits, see Newtonian motivations for general relativity for a nonrelativistic treatment and Theoretical motivation for general relativity for a fully relativistic treatment.
Read more about Introduction To Mathematics Of General Relativity: Oblique Axes, Nontensors, Curvilinear Coordinates and Curved Spacetime, Geodesics, Curvature Tensor
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