□h=-16πT

k is [math]\frac{G}{c^4}[/math], I think that's what you're refering to. The tensor you call the curvature tensor isn't actually THE curvature tensor, it's a tensor constructed from contractions of the Riemann curvature tensor that automatically conserves energy-momentum, but it does essentially give the curvature. For a fluid the SE tensor describes the dyamics of the system, i.e. energy-density, energy-flux, momentum-density, momentum-flux etc. One definition that you may find for a general SE tensor is [math] T^{\mu\nu}=\frac{1}{\sqrt{-g}}\frac{dS}{dg^{\mu\nu} } [/math] Where [math]g^{\alpha\beta}[/math] is the metric, g is its determinant and S is the action for the system.

I've just got the first of those volumes, and they are brilliant.

delete please.

Sounds like a pretty good idea. I'd certainly offer to contribute, that is if any one wanted my help.

Oh yeah, didn't think to simplify it, stupid me. Yeah i get 2.

The energy-momentum four-vector is the same as the 4-momentum vector. The 4-momentum vector has as its time component the energy of the frame and so gets its other name "energy-momentum" four-vector.

That's what I meant by theory, just couldn't think of another way of putting it. Thanks for pointing that out.

Well special relativity starts off pretty basic and then develops into the idea of mass-energy equivalence. SR deals with inertial frames in a flat Euclidean space-time; GR with the geometry of curved space-time.

Yes, I find it is. It's better than being told that such and such happens as a result of GR without being given any justification.

It's the nature of the (convex) lens in our eye: if objects are beyond the focal length of the eye then they appear smaller than they actually are. You can find this in any book treating optics.

Ok well those books are ok if you just want to know the theory side of the big theories in modern physics, but that's boring. If you want to get into the interesting side of GR etc, i.e. the maths, then you should get a couple of books on the calculus of many and single dimensions, abstract algebra (set and group theory, linear algebra etc.) and differential geometry. Those prerequisites will suffice for any introductory course in general relaltivity. As for superstring theory and the like, generally a post grad/grad course, you'll need an education in complex analysis and spinor algebra/calculus. As a basis for all advanced physics you need a fairly decent knowledge of classical mechanics. A good book I have on single dimensional calculus and a bit of multi-D is "The Calculus Tutoting Book"- C&R Ash. A damn good mathematics book for university physics courses is "Mathematical Methods for Physics and Engineering"- Riley et al, which gives a fairly detailed exposition of most of the topics i mentioned above, plus more. As for differential geometry I have "Geometrical Methods of Mathematical Physics"- B. Schutz, an excellent book demanding very few prerequisites and that covers all aspects of differential geometry, from Riemann to Cartan. The universal text for general relativity is "Gravitation"- Misner et al, a big book with a hefty price tag. I learnt GR/SR at university level from "A first course in general relativity"- B. Schutz, which covers the differential geometry required for basic GR before going into the physics.

Cheers guys.

Ok, well I'll put something together about the basics and then I think it would be fairly interesting to move onto manifolds so that we can get bits about differential forms and the lie and covariant derivatives etc in.

Seeing as this thread has more or less dried up, have a read of this .pdf and we can make any problems you have with it topics of discussion. The .pdf has subsequently been published as a book on GR, so it will be better at explaining topics better than I will. Carrol lecture notes on GR I've read the bits of interest to me and I must say he's a good writer.

Could anyone give me a brief exposition, or direct me to books/resources, on spinor algebra/calculus? Thanks in advance

Right then, Johnny, you want to get this going again? That is if no admins object.

You could use the Binomial theorem for non-natural powers. Can't be arsed to quote it for you, do a google.

I don't mind when we continue. Just post in that thread when you want to start again and if there's anything you've been wondering about etc. I've only read about quaternions up to the ol' "Brougham Bridge" equations really, not bothered really going into them, I have too much other stuff on the go. I don't know much about mathematics history, bit more interested in the mathematics itself. The 1/2 is important because it means that the einstein tensor obeys the Bianchi identities and hence conserves local energy and momentum.

Johnny5, the Einstein tensor has the coefficient of the ricci scalar and metric as a half not a quarter. [math] G^{\alpha\beta}=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R[/math]

The correct addition of velocity law is not the Gallilean addition law: the velocity isn't simply v1+v2. The speed of light remains constant for all inertial observers.

'Damn 'tex. G=8G(pi)T The stress-energy tensor (T) is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity. Just do a google search for einstein's field equations.

'Damn 'tex. G=8G(pi)T The stress-energy tensor (T) is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity.

'Damn 'tex. Here's Einstein's field equations in component form <html>G_αβ=8πT_αβ</html> The stress-energy tensor is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity.

See above for equation. The stress-energy tensor is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity. Google Einstein's field equations. Sorry about the accidental mass posting.

I really enjoyed it, despite its deviation from the plot of the book and such. Can't really say what my favourite bit was. Bill Bailley as the whale and Bill Nighy as Slartibartfast were cool.