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# phys documents (dragged) 13 - 16 Physics Formulary by ir...

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Unformatted text preview: 16 Physics Formulary by ir. J.C.A. Wevers • r > 2 m : u = r 2 m- 1 exp r 4 m cosh t 4 m v = r 2 m- 1 exp r 4 m sinh t 4 m • r < 2 m : u = 1- r 2 m exp r 4 m sinh t 4 m v = 1- r 2 m exp r 4 m cosh t 4 m • r = 2 m : here, the Kruskal coordinates are singular, which is necessary to eliminate the coordinate singularity there. The line element in these coordinates is given by: ds 2 =- 32 m 3 r e- r/ 2 m ( dv 2- du 2 ) + r 2 d Ω 2 The line r = 2 m corresponds to u = v = 0 , the limit x → ∞ with u = v and x → -∞ with u =- v . The Kruskal coordinates are only singular on the hyperbole v 2- u 2 = 1 , this corresponds with r = 0 . On the line dv = ± du holds d θ = d ϕ = ds = 0 . For the metric outside a rotating, charged spherical mass the Newman metric applies: ds 2 = 1- 2 mr- e 2 r 2 + a 2 cos 2 θ c 2 dt 2- r 2 + a 2 cos 2 θ r 2- 2 mr + a 2- e 2 dr 2- ( r 2 + a 2 cos 2 θ ) d θ 2- r 2 +...
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