... x2,weget,∂0log[h]=∂tlog[h]=09∂3log[h]=∂φlog[h]=0∂ 1 log[h]=∂ 1 log[(e 1 1) 1/ 2]= ∂ 1 log[(E 1 1) 1/ 2]∂2log[h]=∂2log[(e22) 1/ 2]= ∂2log[(E22) 1/ 2]Consequently we only need e 1 1and e22to be appropriately ... to∂µlog[h]=− 1 2E b λ∂λe b µ(2 .11 )Clearly the existence of h and the success of the factorisation ansatz depends on the inte-grability of (2 .11 ). However, the integrability of (2 .11 ) is not ... s,gµνdxµdxν= g00(x 1 ,x2)dt2+2g03(x 1 ,x2)dtdφ+ g33(x 1 ,x2)dφ2+ g 11 (x 1 ,x2)(dx 1 )2+ g22(x 1 ,x2)(dx2)2+2g 12 (x 1 ,x2)dx 1 dx2if we choose coordinates...