TEC-0-3-35 | |||
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CAN-3-1-22 |
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【SEOテキスト】04.12.6,CAN-3-1-22-18,19,dX1=dx1+(g/c2)x4dx4,dX2=dx2,dX3=dx3,dX4=dx4,-ημνdXμdXν=(dx1)2+2(g/c2)x4dx1dx4+(g2/c4)(x4)2(dx4)2+(dx2)2+(dx3)2-(dx4)2,CAN-3-1-22-25〜28,dx'4=exp[-(g/c2)X1]・dx4-(g/c2)x4exp[-(g/c2)X1]・dx1-(g2/c4)(x4)2exp[-(g/c2)X1]・dx4,(dx'4)2=exp(-2gX1/c2)×[(dx4)2+(g2/c4)(x4)2(dx1)2+(g4/c8)(x4)4(dx4)2-2(g/c2)x4dx1dx4+2(g3/c6)(x4)3dx1dx4-2(g2/c4)(x4)2(dx4)2]=exp(-2gX1/c2)×[1-(g2/c4)(x4)2]×[(dx4)2-(g2/c4)(x4)2(dx4)2-2(g/c2)x4dx1dx4]+(g2/c4)(x4)2exp(-2gX1/c2)・(dx1)2∴(dx'1)2/1-g2(x4)2/c4+(dx'2)2+(dx'3)2-exp(2gX1/c2)/1-g2(x4)2/c4(dx'4)2=(dx1)2+(dx2)2+(dx3)2+2(g/c2)x4dx1dx4-[1-(g2/c4)(x4)2](dx4)2宇田雄一 |
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