This video (GR - 17) starts with a fairly lengthy introduction to explain ‘where we are going’ - namely the journey from discussing the ‘Riemann Tensor’ to the ‘Ricci Tensor’ and then to the ‘Curvature Scalar’.
After almost 8 minutes of this introduction, we then begin by thinking about “Parallel Transport”, and the way in which vectors may change under such ‘transport’ if the space (or space-time) is curved. This idea leads on to a rather detailed explanation of the Riemann Curvature Tensor. However, the need for the Ricci Tensor is then suggested, and the discussion proceeds to show how that ‘comes out of’ the Riemann Tensor. Similarly, the third measure of curvature, the Curvature Scalar (‘Ricci Scalar’) is shown to be derived from the Ricci Tensor.
This video is part of a series of videos on General Relativity (GR-01 to GR-20), which has been created to help someone who knows a little bit about “Newtonian Gravity” and “Special Relativity” to appreciate both the need for “General Relativity”, and for the way in which the ‘modelling’ of General Relativity helps to satisfy that need - in the physics sense.
The production of these videos has been very much a ‘one man band’ from start to finish (‘blank paper’ to ‘final videos’), and so there are bound to be a number of errors which have slipped through. It has not been possible, for example, to have them “proof-watched” by a second person. In that sense, I would be glad of any comments for corrections ……. though it may be some time before I get around to making any changes.
By ‘corrections and changes’ I clearly do not mean changes of approach. The approach is fixed - though some mistakes in formulae may have been missed in my reviewing of the final videos, or indeed some ‘approximate explanations’ may have been made which were not given sufficient ‘qualification’. Such changes (in formulae, equations and ‘qualifying statements’) could be made at some later date if they were felt to be necessary.
This video (and channel) is NOT monetised
25 янв 2023
