﻿ Erratum in general relativity book

# Erratum in book published January 10, 2023

Please forward to people who bought the book.

 Important   ( red = incorrect   -->   blue = correct ) page 52, equation (27) on the right-hand-side: Tmn -> Tpq page 65, We shall consider the dot products of V with the e1's -> We shall consider the dot products of V with the ei's page 136, line 6: Z3 -> X3 page 143, equation (28), denominator in the definition of cosine: 2i -> 2. And at bottom of page 145: no i in the denominator of the sine. page 166, the d for differentials are missing see image page 179, line 12: the trajectory with shortest proper time -> the trajectory with smallest action. And line 18: to minimize the proper time -> to minimize the action page 191, second paragraph from bottom, formula for the Lagrangian. Inside the square root, it should be simply d tau2. See image page 192, equation 36. The one occurrence of $\dot{r}$, in the denominator, should be $\dot{r}^2$ pages 274-275, figures 8, 9 and 10, slanted line on bottom right: U+ = -1 -> U- = -1 page 285, lines 6 and 7: The interior of the shell is the part of the curve to the right of the shell. -> The interior of the shell is the part of the curve to the left of the shell. page 311, bottom line: Tm0=Tm0 -> Tm0=T0m. And at top of page 312, connect Tm0 with Tm0 -> connect Tm0 with T0m page 328, line 5 from bottom: But outside the solar Schwarzschild radius the geometry is exactly the same -> But outside the solar radius the geometry is exactly the same. And line 3 from bottom: Far away from the Schwarzschild radius -> Far away from the radius page 333, 1st sentence of second paragraph: Notice that neither the Ricci tensor nor the Riemann tensor have to be zero. -> Notice that the Riemann tensor doesn't have to be zero. page 342, the tensor hmn should read like on this image page 349: bottom line: and hyx is the the opposite -> and hyx is the same. page 350: (consequence of the above correction): the matrix at the top of the page should be symmetric Cosmetic page 137, legend to figure 8:    proper time tau -> proper time Δ tau (put the correct Greek character, which for some reason my html doesn't want to display) page 152, line 3:    motion for a geodesic -> motion along a geodesic page 175, line 1 (beneath first equation):    want to minimize -> want to "extremelize" page 184, line 1:    we wrote for tau2 -> we wrote for d tau2 page 212, line 5 from bottom:     is differentiate the left-hand side -> is differentiate the right-hand side page 267, line 14: and time and proper time are almost the same -> and coordinate time and proper time are almost the same page 312, misspelling : paragraph above equation (23).  "What we have learned {it => is}" page 341, on figure 2: x = 0 -> X = 0 ; and x' = 0 -> X' = 0 pages 338, 339, 343, equations (11), (12), (19), (20): the denominators of the derivatives should have curly d's

Many thanks to Floe, Emmanuel, Mike, Tobias and François, for pointing out some of these errors.

If you find other typos or mistakes, please contact André Cabannes: andre.cabannes@gmail.com