﻿ 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. 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, and Tobias, for pointing out some of these errors.