Basic introduction to the mathematics of curved spacetime | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Introduction_to_the_mathematics_of_general_relativity


00:00:59 1 Vectors and tensors
00:01:09 1.1 Vectors
00:02:06 1.2 Tensors
00:02:50 1.3 Applications
00:04:33 1.4 Dimensions
00:05:08 1.5 Coordinate transformation
00:07:54 2 Oblique axes
00:08:23 3 Nontensors
00:09:18 4 Curvilinear coordinates and curved spacetime
00:10:37 5 Parallel transport
00:10:47 5.1 The interval in a high-dimensional space
00:13:21 5.2 The covariant derivative
00:14:08 5.3 Parallel transport
00:14:35 5.4 Christoffel symbols
00:14:51 6 Geodesics
00:15:01 7 Curvature tensor
00:15:52 8 Stress–energy tensor
00:17:01 9 Einstein equation
00:18:48 10 Schwarzschild solution and black holes
00:19:33 11 See also
00:21:01 12 Notes
00:22:20 13 References



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SUMMARY
=======
The mathematics of general relativity is complex. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone. In relativity, however, an object's length and the rate at which time passes both change appreciably as the object's speed approaches the speed of light, meaning that more variables and more complicated mathematics are required to calculate the object's motion. As a result, relativity requires the use of concepts such as vectors, tensors, pseudotensors and curvilinear coordinates.
For an introduction based on the example of particles following circular orbits about a large mass, nonrelativistic and relativistic treatments are given in, respectively, Newtonian motivations for general relativity and Theoretical motivation for general relativity.