【SEOテキスト】宇田雄一「古典物理学」3-1-2運動方程式の解,以下の定理①②③④⑤が成り立つ。①平坦な時空∀f∈F5;∀n∈N;∀Z∈F4,n;[【1】and【2】]⇒【3】【1】∃a∈R(N03);(det
a<0)and[∀(i,j)∈N03;a(i,j)=a(j,i)]and[∀(ξ,i,j,4)∈N5;f(ξ,i,j,4)=a(i,j)]【2】Z(N3)=0【3】e7(f,Z,0)②シュヴァルツシルト時空∀f∈F6,1;∀m∈R(1);[【1】and【2】and【3】and【4】and【5】]⇒【6】【1】f(N4,1)=0【2】∀(ξ,i,j,4)∈N5;i=j∈3⇒f(ξ,i,j,4)=-1-m(1)/(4π)/|ξ(3)|-m(1)/(4π)・[ξ(i)]2/|ξ(3)|2【3】∀ξ∈N01;f(ξ,4,4,4)=1-m(1)/(4π)/|ξ(3)|【4】∀(ξ,i,j,4)∈N5;(i≠4
and j=4)⇒f(ξ,i,j,4)=0【5】∀(ξ,i,j,4)∈N5;4≠i≠j≠4⇒f(ξ,i,j,4)=-m(1)/(4π)/|ξ(3)|-m(1)/(4π)・ξ(i)ξ(j)/|ξ(3)|2【6】e7(f(N5),f(N4,1),m)
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