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waterfall
waterfall is offline
#191
Feb23-12, 07:52 PM
P: 381
Quote Quote by bhobba View Post
Well I am not sure I want to go into this because my interests these days is on the foundations of QM, but no I do not agree linearised gravity does not imply GR. One of the first textbooks I ever got on GR many many moons ago was Ohanian - Gravitation and Space Time a copy now falling to pieces I still have. That book takes an entirely different view of GR, first deriving linear GR from field theory via analogy with with EM then showing how full GR can be derived from the linear equations - you will find the details in Chapter 7 of that book. However something does go into it - namely the following assumption from page 380 - the equation is of second differential order and is linear in second derivatives. That pretty much follows from the fact it should be derivable from a Lagrangian containing only first order derivatives - which GR can be -but usually isn't - the covariant form based on the very elegant Einstein-Hilbert action is usually used - but is of second order. However when the variation is done terms linear in second order - which the Einstein-Hilbert action is - make no contribution so can be removed - which leaves a non covariant action but only containing first order terms. Bottom line is this means the EFE's must be linear in second order. A full discussion of this can be found in Chapter 8 of Lovelock and Rund where the most general form is given on page 321 of that reference (its pretty ucky).

That's about all I really want to say about the issue because GR is the furthest thing from my mind or interests right now and refreshing my mind on this stuff took a good couple of hours.

Thanks
Bill
Juanrga, Haelfix or other anti-spin twoners, can you please point out the mistakes in the analysis above without showing any other references but directly addressing the issues? Let's get to the bottom of this. Thanks.