Kruskal Co-ordinates (An Introduction)

Here (GR - 15), we start with some further discussion of the previously introduced Schwarzschild Metric, highlighting the problem that the speed of light is measured (by an outside observer) to decrease as an object approaches a concentrated mass (black hole). To rectify this, a Co-ordinate Transformation is suggested to a new set of co-ordinates called “Kruskal Co-ordinates”, which make sure that the ‘outsider’ always measures the speed of light to be the same everywhere. This, of course, has other consequences for measurements, not least for how the ‘Event Horizon’ is depicted in space-time diagrams, and these are discussed. In particular, the benefit of diagrams with Kruskal Co-ordinates is explored in relation to communication between various objects outside (and inside) the Event Horizon of a black hole. 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