Mathematics of general relativity | Wikipedia audio article
Channel: wikipedia tts
Date: 08/12/2018

This is an audio version of the Wikipedia Article:
Mathematics of general relativity


00:00:31 1 Tensors
00:01:27 2 Spacetime as a manifold
00:02:52 2.1 Local versus global structure
00:03:46 3 Tensors in general relativity
00:09:03 3.1 Symmetric and antisymmetric tensors
00:10:57 3.2 The metric tensor
00:12:56 3.3 Invariants
00:14:48 3.4 Tensor classifications
00:15:28 4 Tensor fields in general relativity
00:18:19 5 Tensorial derivatives
00:19:20 5.1 Affine connections
00:24:18 5.2 The covariant derivative
00:33:44 5.3 The Lie derivative
00:42:22 6 The Riemann curvature tensor
01:00:59 7 The energy–momentum tensor
01:01:40 7.1 Energy conservation
01:02:35 8 The Einstein field equations
01:05:08 9 The geodesic equations
01:08:18 10 Lagrangian formulation
01:08:57 11 Mathematical techniques for analysing spacetimes
01:09:20 11.1 Frame fields
01:10:01 11.2 Symmetry vector fields
01:10:46 11.3 The Cauchy problem
01:11:38 11.4 Spinor formalism
01:12:16 11.5 Regge calculus
01:12:56 11.6 Singularity theorems
01:13:23 11.7 Numerical relativity
01:14:03 11.8 Perturbation methods
01:14:29 12 See also
01:14:40 13 Notes



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SUMMARY
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The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying and formulating Albert Einstein's theory of general relativity. The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics of general relativity.

Note: General relativity articles using tensors will use the abstract index notation.