11 The Kaluza-Klein Black Hole

Chapter 11
The Kaluza-Klein Black Hole

Page 315, Eq. (11.106) V should be replaced by l in hte second term of the r.h.s.

$( ) Gˆab = eaμebν 2∂[μVν] + 2l∂[μA ν] , (11.106)$
Page 315, Eq. (11.114) should be replaced by G in the Chern-Simons term (the last one):

$∫ -2πℓ-- 4 ∘ --- { 1 -2 2 1 2 2 1 2 S = 16πG (ˆd) d x |g |k R + 2k (∂l) - 4k F (A ) - 4G N } (11.114) + -√k-√1l-ϵ[G - 2A ∂l]2 . 4 3 |g|$
Page 336, Eq. (11.198). The second = sign should be a ∈ sign:

$1 T 2 ω = 2πℓ ⃗ω ⋅⃗z , ⃗ω ∈ ℂ ,$