By Thomas A. Moore

A common Relativity Workbook is a textbook meant to help a one-semester undergraduate path on common relativity. via its particular workbook-based layout, it permits scholars to boost a high-quality mastery of either the physics and the assisting tensor calculus through guiding them to paintings in the course of the implications. the maths is brought steadily and in a very actual context. each one bankruptcy, that is designed to correspond to at least one type consultation, includes a quick assessment of the innovations with no obscuring derivations or info, through a chain of packing containers that advisor scholars during the strategy of operating issues out. This active-learning procedure permits scholars to strengthen a safer mastery of the fabric than extra conventional techniques. greater than 350 homework difficulties help additional studying.

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40) W 0 SS WW SS 0 WW 0 0 T X T X Let’s assume that the proton energy is very large in our frame, so that E p >> m p , do the calculation, and then check that our answer is consistent with this assumption. Since m2p = E2p - p2px, , this approximation implies that 2 2 c p2px = E2p - m2p . E2p so p px . 39, and solve for Ep, you will find that Ep . 42) Since m p = 938 MeV and mr = 135 MeV, you can show that E p � 2 × 1020 eV. This is the GZK cutoff for proton energies: protons with energies greater than this should lose energy to collisions with CMB photons when traveling between galaxies.

3 ). We will find the four-velocity a very useful quantity in the future, so it is wise to be very familiar with the equations in this section. 27 28 3 Four-Vectors Four-Momentum . 13) p = mu W S p y W S mu y W S mvy W 2 S W S W S 1-v W S W S W S W S p z W S mu z W S mvz W 2 W S X 1-v T X T T X In modern special relativity and general relativity, we consider an object’s mass m to be frame-independent. 3 by m to see that this is true), meaning that p is also a four-vector. 14) Conservation of Four-Momentum .

A. Show that in frame S, four-momentum is conserved by this collision as long as the mass M of the final object is not 2m but rather 2m/ 1 - v2 . b. Show that four-momentum is also conserved in S´. 5 The energy of a photon is related to its wavelength m by the expression E = h/m (in GR units) where h = 1240 eV·nm. Imagine that a photon has a wavelength of m0 in the frame of the source. An observer is moving with speed v away from the source. a. Use a Lorentz Transformation of the photon’s fourmomentum to find the photon’s energy and wavelength in the frame of the observer.

### A general relativity workbook by Thomas A. Moore

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