Schwarzschild Metric (An Introduction) – Radial & Orbital Motion near a Black Hole
After a short revision of some of the ideas from the previous video (GR - 12) concerning hyperbolic co-ordinates and acceleration, ‘mass’ is introduced in such a way that it can produce the same acceleration in the region under discussion. This leads to a simplistic derivation of a metric which has some of the characteristics of the Schwarzschild Metric. The ‘Schwarzschild Radius’ and the ‘Event Horizon’ are seen to be problematic for the ‘signature’ of this metric, and a solution is offered, with only a cursory justification, which then leads to the Schwarzschild Metric itself.
The Schwarzschild Metric is then explored in a little detail, in order to get a ‘feel’ for it, before two important scenarios are investigated. Firstly, radial motion towards or away from a black hole is discussed - for objects with mass and for light. Comparisons are made with the results that Newtonian gravity would suggest for such motion. Secondly, orbital motion of light (but not mass) around a black hole is discussed - leading to the idea of the ‘photon sphere’.
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.
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