# What is Schutz: Definition and 35 Discussions

Schutz (German: shelter, protection) is a German surname, related to Schütz (which needs to be spelled Schuetz without umlaut ü). Notable people with the surname include:

Alfred Schutz, Phenomenological philosopher and sociologist
Bernard F. Schutz (born 1946), physicist
Dana Schutz, painter in New York
David Schütz, Israeli writer
Guillermo Schutz (born 1980), Mexican sports announcer
Heinrich Schütz, German composer
Herbert Schutz (1937-2018), German-born Canadian philologist
Johan Christher Schütz, Swedish singer and composer
Katelin Schutz, physicist and cosmologist
Maurice Schutz, French actor
Peter W. Schutz (born 1930), Porsche manager
(1657–1742), German writer
Roger Louis Schutz-Marsauche (Frère Roger, 1915–2005)
Susan Polis Schutz, American poet
William Schutz, psychologist in the 1960s

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1. ### I When did the consensus on the maximum recession speed in cosmology change?

In the last chapter of Schutz devoted to Cosmology, Schutz writes So it seems that in 1985 it was assumed as obvious that the recession speed could not exceed ##c##. The consensus seems to have swiftly changed. When did that happen? Was it debated at all?
2. ### I Is this just a typo in Schutz' book on General Relativity?

I'm wondering is I'm missing something, or this should be " a non-zero component"?
3. ### A Some questions about the derivation steps in the Gravitational deflection of light section in Schutz

In the screenshots below there are the equations (11.49) and (11.53). I don't understand how did he derive equation (11.53) from Eq.(11.49)? From (11.49) I get: ##d\phi/dy= d\phi/du du/dy = (1/b^2-u^2+2Mu^3)^{-1/2}(1+2My)##. It seems he neglected the ##2Mu^3## since ##Mu\ll 1##, so ##y\approx...
4. ### I Inquiry about a derivation in "A First Course in GR" by Schutz

on page 269 it's written in the second edition of Schutz's textbook that ##(10.69)p_c/\rho_c=\beta (2-5\beta)^{-1}##. Demanding that this be less than ##1/7## gives: ##(10.70) 0<\beta < 1/6## Now, if I am not mistaken on page 268 in equation (10.57) the condition should be ##p_c/\rho_c >1/7##...
5. ### I Bernard Schutz Proves Invariance of Interval

I've been going through Bernard Schutz's A First Course in General Relativity, and I'm hung up on his "proof" of the invariance of the interval. At the beginning of section 1.6, he claims that he will prove the invariance of the interval, and after a few lines shows that the universality of the...
6. ### Relativity Where Can Hobbyists Access the Full Solutions Manual for 'A First Course in General Relativity' by Schutz?

I'm self-studying various physics topics (as a hobby) and currently enjoying "A first course in general relativity" by Schutz. I also have the students manual for this book by Scott which provides the answers to a selection of the exercises in the book as well as some additional material. For...
7. ### Derivation of Equation (1.6) in Schutz: A First Course in GR

Homework Statement From pages 10--11 in "A First Course in General Relativity" (Second Edition) by Bernard Schutz: Given $$\Delta\overline{s}^2 = \phi\left(\textbf{v}\right)\Delta s^2,$$ where ##\Delta \overline{s}^2## is the interval measured between two events in frame ##O'##, which is...
8. ### Relativity Learning Einstein's General Relativity

So, I'm going to learn general relativity but I'm confused in which book I start with Bernard Schutz book seems excellent but I'm more interested in d'Inverno book, And Misner/Throne Book Seems complete but its giant and good for reference, So I think I will go with d'Inverno , but first I need...
9. ### I Understanding Schutz's Geodesic Deviation Eq. 6.84

I have some problem understanding the section on "Geodesic deviation" in schutz, more specifically I'm confused by eq. 6.84: Eq 6.84 reads (ξ is the 'connecting vector' from one geodesic to Another, V is the tangent vector): We can use (6.48) to obtain ∇V∇Vξα = ∇V(∇Vξα) = (d/dλ)(∇Vξα) =...
10. ### Schutz GR Book, Question about World line.

This isn't homework, nor is it an exercise problem; merely a question about a diagram. Re: B.Schutz book "A First Course in General Relativity" 2nd Edition, (Asian print version), page 5, Figure 1.1 "A spacetime diagram in natural units". From section 1.4 Spacetime diagrams: A world line is...
11. ### I Are many exercises in Schutz just too hard?

Dear all, I am self-studying GR using A First Course in General Relativity by Bernard F Schutz. I am halfway through the course, trying to solve all the exercises. But I worry that I can solve maybe 80% of them, the remaining 20% I find them just too hard. I know I am no genius, and I don't have...
12. ### GR Schutz: Why r Must Decrease in Black Hole Section?

Schutz states in his book in the black hole section that: At r<2GM, r is a timelike coordnate, while t has become spacelike: even more evidence for the funniness of t and r! Since the infalling particle must follow a timelike world line, it must constantly change r, and of course this means...
13. ### Schutz page 294 (Deflection of light)

Hello Everyone, I am working through Schutz's A first Course in General relativity. On page 294 he defines the equations (11.52) to simplify equation (11.49) and calculated the deflection of light around the sun. I know that he wants to simplify it and also to preserve the effect of the mass M...
14. ### Heuristic Evaluation of Stress-Energy Tensor

I've been reading through Schutz's A First Course in General Relativity, and my solution to a particular problem has got me wondering if I'm being careful enough in my approach. The problem states: Show that, in the rest frame ##\mathcal{O}## of a star of constant luminosity ##L## (total energy...
15. ### Can the Tensor Integral in GR be Bounded by a Region Outside of d^{3}x?

Dear all, I am self studying GR and stuck on problem (23) on page 108/109. I am trying to do all of them. First I will start with (a) so you guys can breath while laughing at my attempts at (b) and (c) :blushing: (a) Attempt The tensor in the equation is bounded in the d^{3}x region. Outside...
16. ### Schutz First Course in GR Problem 15b, chapter 1. Mistake?

Homework Statement Suppose that the velocity of an observer O' relative to O is nearly that of light, |v|=1-ε, 0<ε<<1. Show that the Lorentz contraction formula can by approximated by: ∆x≈∆x'/√(2ε)Homework Equations Lorentz contraction, ∆x=∆x'/γThe Attempt at a Solution I think it should be...
17. ### Study buddies for 'A First Course in General Relativity' by B. Schutz

Hi, I decided to learn about relativity with this book, and I'm looking for people who would like to read it with me and discuss :thumbs:. Since I'm a little busy at the moment the pace will be quite slow, let's say about a chapter each two weeks (or more later for more advanced chapters)...

19. ### Relativity A First Course in General Relativity by Schutz

Author: Bernard Schutz Title: A First Course in General Relativity Amazon Link: https://www.amazon.com/dp/0521887054/?tag=pfamazon01-20 Prerequisities:
20. ### Calculation on hawking radiation in schutz (pg 324)

on pg 324 of Schutz's "A First Course in General Relativity", i am having a little trouble with the integral (11.100). the book says that to first order in \epsilon , the answer should be 2\sqrt{2M\epsilon} but i keep getting \sqrt{2M\epsilon} . i am missing that factor of 2 somehow. the...
21. ### Comparing Hartle, Schutz, and Ohanian for GR Beginner

I'm going to attempt to start a beginner GR book since we're covering it in Modern Physics and I've been covering the material up a notch so far (I did the SR by reading Spacetime Physics by Taylor and Wheeler & I've already read Griffith's for the Qmech section etc.) I don't intend to finish an...
22. ### Schutz 4.5, p. 100: A differential equation

Bernard Schutz, in A First Course in General Relativity, section 4.5, p. 101 (in this edition), writes that \mathrm{d}\rho-(\rho+p)\frac{\mathrm{d}n}{n} "depends only on rho and n." Is he saying \mathrm{d}\rho-(\rho+p)\frac{\mathrm{d}n}{n} = f(\rho,n) where f : {scalar fields on...
23. ### Supplementary Reading for First GR Course: Schutz vs Hartle?

I hope this is the right forum to post this... I'm going through Wald's book in my first graduate level GR course, and am looking for lower level supplementary reading. I have a relatively strong math background, so Wald's language suits me well, but sometimes I feel like I need more...
24. ### Schutz - A First Course in GR - Simple Summation Question

Hello all, In the book "A First Course in General Relativity" by Schutz (1985 Edition) in chapter 2 there is a problem concerning summation that has me confused. Note: This is not homework, just an interest of mine. The given quantities are: A = (5,0,-1,-6) B = (0,-2,4,0) C = [ 1 0 2 3...
25. ### Energy-stress tensor integration proof (from schutz ch.4)

Homework Statement Use the identity T^{\mu \nu}_{ ,\nu} = 0 to prove the following results for a bounded system (ie a system for which T^{\mu \nu} = 0 outside a bounded region of space), \frac{\partial}{\partial t}\int T^{0\alpha}d^{3}x = 0 Homework Equations The Attempt at a Solution The...
26. ### Schutz: Next Steps in General Relativity

Hi, I have just read (well read most of :) ) Schutz First Course in Gen Rel, what would be a good book to go on from after this? I thought Schutz was pretty good on the intro to tensors and diff geo, since it approached the subject from the index free way, which I found more satisfying than...
27. ### Solve Eq. (9.58) on Schutz Page 246 - A First Course in GR

Here is a question from problem 26 part a on page 246 of "A First Course in GR" by Schutz. I doubt that it can be answered by someone without a copy of the book, but I have thought that before and been wrong. If someone without the book wants to help and needs more information then of course I...
28. ### Solving Schutz Problem 23 (a & b): T^{\mu ν} Identity

This time I am asking for help on a problem. I think I have an answer for problem 23, part (a), but I would like verificiation. I don't have a solution for part (b). Problem 23: Use the identity T^{\mu \nu}{}_{,\nu} = 0 to prove the following results for a bounded system (i.e. a system for...
29. ### GR: A First Course Q: What is "That Region" on Page 226?

Here is a question that requires you to have a copy of the book (A First Course in GR) to answer it. On page 226, near the bottom of the page is this sentence: The second assumption is called the slow-motion assumption, since it implies that the typical velocity inside the source region...
30. ### Schutz, page 226 - Black hole formation

This question involves the following statement in Schutz, A First Course in GR, but you don't need to have a copy to answer it. He says that in the formation of a black hole from a supernova explosion, we should expect gravity waves of amplitude M/R, where M is the mass and R is the distance...
31. ### Verifying Equations 9.45 & 9.46 in Schutz, pg. 224

This question is just for those who have a copy of Schutz, A First Course in GR. I have tried to plug equations 9.43 and 9.44 into equation 9.42 in order to verify equations 9.45 and 9.46. So far, I have not been successful. However, I have come to the conclusion that probably 9.45 is incorrect...
32. ### Simplifying Equations for Lorentz Boosts with Small Beta

I got so much excellent help from my last question that I have decided to take advantage as much as I can. Here is another question. On page 202, I combine equations 8.18 and 8.19 and change bars for primes (to match eqn. 8.22) g_{\alpha' \beta'} = \eta_{\alpha' \beta'} +...
33. ### Question from Schutz, A First Course in GR

Can someone help me understand something on page 220 of the book 'A First Course in General Relativity' by Bernard Schutz? Near the middle of the page, the line element is given as ds^2 = -dudv + f^2(u)dx^2 + h^2(u)dy^2 (I changed g to h so I can talk about the metric tensor) which I...
34. ### Gravitation from the Ground Up - B.F. Schutz

Has anyone read Gravitation from the Ground Up, B.F. Schutz? What did you think of it? Pete
35. ### Triangle on a sphere (Schutz, 6.10)

How to proceed to prove this?