Corrections

I have sent this list of eight corrections I have found to date to the author, Sean Carroll. There is one extra (p.148) which I only found by peeking at a reprint of the question.

Chapter 1

p.24 just before equation (1.68) it reads "There is also the Levi-Civita symbol a (0,4) tensor." Surely it is not a tensor.

Chapter 2

p. 80 Equation (2.64) should be λ = -cot^-1 t (https://www.general-relativity.net/2018/12/commentary-27-causality.html part 2)

p.81 Figure 2.26 fig 2.26 shows a singularity at a point p and the text discusses a point p that is in the future of the singularity. (https://www.general-relativity.net/2018/12/commentary-27-causality.html part 2)

Possible error

p. 82 Equation (2.66) could be much simpler if μ'₁ μ'₂ ...μ'_n = 01...(n-1). (It's more streamlined.)
This is trued but if the simplified for was given, the next equation would not work! (GK)

Chapter 3

p.96 equation (3.10) for the connection transformation law. The + sign should be -. (https://www.general-relativity.net/2019/03/the-christoffel-symbol.html)

Possible error

p.99 definition of torsion-free (connection symmetric in lower indices) given as Γ^λ_μν = Γ^λ_(μν). Surely Γ^λ_μν = Γ^λ_νμ. would be clearer? (https://www.general-relativity.net/2019/03/the-christoffel-symbol.html)

p.148

Exercise 6(a) should end "Which clock ticks faster?" I picked this up from http://web.physics.ucsb.edu/~phys231A/231A/Homework_files/hw4_solutions.pdf.

Appendices

p. 427 equation (A.11) ϕ is used to mean two different things: a map and a polar coordinate. (https://www.general-relativity.net/2018/09/commentary-on-appendix-mapping-s2-and-r3.html)