Errata A. Rendall

Here I list errata to my book "Partial Differential Equations in General Relativity".
p. 7 In l. 16 'In discusses' should be 'It discusses'

p. 24 In equation (2.25) the index 'a' on the left hand side should be 'b'. The indices of the metric on the following line should be upper indices.

p. 26 In the last term in equation (2.35) the indices 'a' and 'c' should be interchanged in the second factor (i. e. it should be \nabla_c\beta^a).

p. 30 On this page 'variational derivative' should be 'partial derivative' and in the equations (3.1) and (3.2) the symbol 'delta' for a variational derivative should be replaced by that for a partial derivative

p. 41 In the second sentence the of Section 3.3 'The matter fields' should be replaced by 'The basic matter fields' and the third sentence should be replaced by: 'The pressure p is related to them by an equation of state p=f(\mu,s).'

p. 44 In (3.37) the quantity p^0 should be p_0

p. 44 In (3.42) there should be an extra factor -|det g|^{-1/2}p_0

p. 45, l. 27 In the definition of s there should be an overall minus sign

p. 46, l. 5 The lower case omega should be a capital omega

p. 46, l. 14 definition of Israel molecules should not be s but [s(s-4)]^{-1/2}\Gamma (\theta) for a function \Gamma

p. 65 In l. 24 the transformation of y and z to -y and -z should be the transformation of x and y to -x and -y

p. 113 'Great caution is need' near the bottom of the page should be 'Great caution is needed'

p. 119 In equation (7.2) the lower case f should be an upper case f

p. 121 The sentence 'This is a general property of elliptic systems with smooth coefficients' should be replaced by 'This is a general property of elliptic systems with smooth coefficients, the gain being k derivatives when the system is of order k'

p. 122 in equation (7.7) log r should be replaced by -log r

p. 123 'the index is zero' should be 'the index is dim B_1 -dim B_2'

p. 134 In l. 12 the functions u_0 and u_1 should be \phi_0 and \phi_1

p. 165 In equation (8.57) k should be replaced by -k

p. 170 In equation (9.1) there should be an overall factor -1/2 on the right hand side

p. 175 In the second line psi' should be phi'

p. 183 In the last line 'intepretation' should be 'interpretation'

p. 190 In equation (10.12) k should be replaced by -k

p. 219 In l. 21 'there is black hole' should be 'there is a black hole'

p. 202 In l. 17 [0,T^*) should be [t_0,T^*)

p. 216 In l. 7 the right hand side of the first equation should be zero

p. 220 In equation (11.19) there is an extra plus sign

p. 224 Before the sentence starting 'A useful orthonormal frame ...' the following sentence should be inserted: For notational convenience define Gamma=G_t+AH_t.

p. 225 In the sixth line from the end of the page P_1 should be P_i

p. 231 In equation (11.73) -2m/t should be +2m/t in both brackets

p. 250 At the beginning of the section 'Further reading' the following sentence should be added: A useful reference for the Einstein-Vlasov system and the mathematics of other equations of kinetic theory is [8].

p.264, [25] 639-637 should be 639-667

p. 271, [131] Raphael, F. should be Raphael, P.

I am grateful to those who helped me find these mistakes: Håkan Andréasson, Yvonne Choquet-Bruhat, Mattias Dahl, Sergio Dain, Jim Isenberg, David Klawonn, Ernesto Nungesser and Hans Ringström.