## CORRECTIONS

In progress ... this page is updated regularly [last update 6 Mar 2018, more to come soon].

• page 9, two lines before Section 1.2 the text should refer to Eq. (1.1) rather than (1.16) [thanks to Peter Lichtner]
• page 16, equation (1.34) there should be no prime on the T of the right-hand side [thanks to Peter Lichtner].
• page 20, there is an extra word `two' in the caption of Fig. 1.2 [thanks to Peter Lichtner].
• page 31, equation (1.94) it should be ℓ in the denominator and not √ℓ [thanks to Leonardo Trombetta]
• page 40, fifth line in Example 1.14, denotes [thanks to Peter Lichtner].
• page 41, Definition 1.19. It should be stated explicitly that the object in the curly brackets is the standard Christoffel symbol used in (1.72) [thanks to Peter Lichtner].
• page 42, first line, `is' should be `in' [thanks to Peter Lichtner].
• page 45, line after (1.155), it should read `brackets' [thanks to Peter Lichtner].
• page 47, second line should be `symbol' [thanks to Peter Lichtner].
• page 47, final line of (1.160), the last minus should be a plus [thanks to Jorge Moreno].
• page 47, second line after (1.161) `terms' [thanks to Peter Lichtner].
• page 54, after equation (1.197) there is a minus sign missing in R22.
• page 56, after equation (1.209) it should say `in the third step' [thanks to Peter Lichtner].
• page 64, Exercise 1.14 the Christoffel symbol after the equation should be replaced using the curly brackets notation [thanks to Peter Lichtner].
• page 85, near the end of that page, Ta should be called Va to be consistent with the subsequent calculation. In the next edition I will rename all Va to Ta as this will be consistent with the previous calculations.
• page 96, in equation (2.103) the term dt2 is missing in the line element [thanks to Hari Patel].
• page 111, line above (3.1) Examples 1.4 is in Sec. 1.2.4 [thanks to Peter Lichtner].
• page 117, one might use a different r in (3.22) to avoid confusion with the radial coordinate used in the other parts of the this section [thanks to Peter Lichtner].
• page 123, first line, inequality (3.42) [thanks to Peter Lichtner].
• page 123, two lines above (3.48), it should read `approach' not `approached' [thanks to Peter Lichtner]
• page 123, there is r2 missing in (3.49).
• page 131, equations (3.78) and (3.79) (embarrassing!) both numbers stated should be without the 0. part, just the numerical values after the decimal point. The text on page 128 is correct, so I am not sure how this one stayed unnoticed.
• page 133, just above (3.86), `transforms' [thanks to Peter Lichtner].
• page 133, equation (3.86), the final term should read +2Mu3 not minus; page 134, equation (3.88). The previous sign change carries over so the second term which should read -u3.
• page 144, after (3.120), one `the' needs to be removed [thanks to Peter Lichtner].
• page 170, second line, `sign of' [thanks to Peter Lichtner].
• page 173, three lines after equation (4.59) the second integration should be from tobs to tobs + δtobs. In the text it says te.
• page 201, at the end of Exercise 4.5 it should read $\Gamma \left(1/2\right) =\sqrt{\pi }$ [thanks to Hollis Williams].
• page 207, equation (5.10), in the second term A and B have to be interchanged [thanks to Hari Patel].
• page 212, in equation (5.35) the Christoffel symbol should be written in the other notation using curly brackets [thanks to Peter Lichtner].
• page 214, equations (5.11), (5.55), (5.57), (5.59), and (5.61) should all carry a minus sign which I overlooked to carry on from (5.11) [thanks to Robert Maco].
• page 232, end of Exercise 3.3, it should refer to Eq. (3.22) [thanks to Peter Lichtner].
• page 253, first line of (5.233) the final Christoffel symbol should have indices 22 and not 33. In the third line there is a comma missing [thanks to Peter Lichtner].