Download General Relativity by Norbert Straumann PDF

By Norbert Straumann

Show description

Read Online or Download General Relativity PDF

Best relativity books

Time and Consistent Relativity: Physical and Mathematical Fundamentals

Time and constant Relativity: actual and Mathematical basics establishes a brand new and unique thought of time relativity, that's absolutely constant. It explains why Einstein’s idea of time relativity is bodily meaningless and mathematically in keeping with tacit inacceptable assumptions, and why it represents the singular case from the mathematical viewpoint.

Bankrupting Physics: How Today’s Top Scientists are Gambling Away Their Credibility

The lately celebrated discovery of the Higgs boson has captivated the public's mind's eye with the promise that it may clarify the origins of every little thing within the universe. it truly is no ask yourself that the media refers to it grandly because the "God particle. " but at the back of closed doorways, physicists are admitting that there's even more to this tale, or even years of gunning the massive Hadron Collider and herculean quantity crunching should no longer bring about a deep realizing of the legislation of nature.

Extra resources for General Relativity

Example text

90) where the spatial endpoints are kept fixed. Instead of the energy functional for gF we can, of course, also use the length functional. This result is useful for calculating the propagation of light rays in gravitational fields. 76) for the metric. 91) dx , 1 + 2φ with dx 2 = (dx 1 )2 + (dx 2 )2 + (dx 3 )2 . Fermat’s principle becomes δ ˙ dλ = 0, (1 − 2φ) x(λ) 38 2 Physics in External Gravitational Fields ˙ denotes the Euclidean norm of dx/dλ. This agrees with the Fermat prinwhere |x| ciple of geometrical optics ˙ n x(λ) x(λ) dλ = 0 δ for the refraction index n = 1 − 2φ.

In spite of this failure we add some further instructive remarks. First, we want to emphasize that the interaction is necessarily attractive, independent of the matter content. 8) where φ is proportional to ϕ and g is a coupling constant. Note first that only g 2 is significant: Setting φ˜ = gφ, we have L=− 1 ˜ μ φ˜ + T · φ˜ + Lmat , ∂μ φ∂ 2g 2 involving only g 2 . Next, it has to be emphasized that it is not allowed to replace g 2 by −g 2 , otherwise the field energy of the gravitational field would be negative.

This has nothing to do with coordinates or frames. For instance, instead of saying: “. . let Ric be the Ricci tensor, u a vector field, and consider Ric(u, u) . ”, one says: “. . let Rμν be the Ricci 5 It is not permitted to introduce in addition to g μν other “external” (absolute) elements such as a flat metric which is independent of g. 22 2 Physics in External Gravitational Fields tensor, uμ a vector field, and consider Rμν uμ uν , . . ” In particular, the number and positions of indices specify which type of tensor is considered, and repeated indices indicate the type of contraction that is performed.

Download PDF sample

Rated 4.95 of 5 – based on 33 votes