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1. For the following line elements and vector V", write down the metric, the inverse metric, and V² = 9μVμVV: dr.² +r²d0², V = (vt, Vr, Vº) = (a, b, c) 1+r² Vμ = (V², V³) = (a, b) a) ds² = −(1+r²) dt² + b) ds² = -dxdy,

1. For the following line elements and vector V", write down the metric, the inverse metric, and V² = 9μVμVV: dr.² +r²d0², V = (vt, Vr, Vº) = (a, b, c) 1+r² Vμ = (V², V³) = (a, b) a) ds² = −(1+r²) dt² + b) ds² = -dxdy,

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For the following line elements and vector V μ, write down the metric, the inverse metric, and find rest on picture

1. For the following line elements and vector V", write down the metric, the inverse metric, and V² = 9vV"V": a) ds² = (1+²) dt² + b) ds²-dxdy, V" = Ꮩ dr² 1+r² +r2d02, V" = (V*,V",V) = (a,b,c) +r²d0², (V*,V*)=(a,b)
Transcribed Image Text:1. For the following line elements and vector V", write down the metric, the inverse metric, and V² = 9vV"V": a) ds² = (1+²) dt² + b) ds²-dxdy, V" = Ꮩ dr² 1+r² +r2d02, V" = (V*,V",V) = (a,b,c) +r²d0², (V*,V*)=(a,b)
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