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alephys

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These are answers submitted by alephys

Just to add another possibility...

alephys 5
November 20 2024
1 1

restart

with(Physics)

g_[[5, 29, 1]]

 

  

"eq1:=g_[~mu,~nu]*Diff(w(r,theta), SpaceTimeVector[mu](X))*Diff(w(r,theta), SpaceTimeVector[nu](X))"

(Diff(w(r, theta), Physics:-SpaceTimeVector[`~mu`](X)))*(Diff(w(r, theta), Physics:-SpaceTimeVector[`~nu`](X)))*Physics:-g_[`~mu`, `~nu`]

 (2)

SumOverRepeatedIndices(eq1)

((Diff(w(r, theta), r))^2*(a^2-2*m*r+r^2)^2+(Diff(w(r, theta), theta))^2*(a^2-2*m*r+r^2)+(Diff(w(r, theta), phi))^2*(-2*m*r+r^2+a^2*cos(theta)^2)*csc(theta)^2-4*(Diff(w(r, theta), t))*(Diff(w(r, theta), phi))*m*r*a-(Diff(w(r, theta), t))^2*(cos(theta)^2*a^4+cos(theta)^2*a^2*r^2+2*m*r*a^2*sin(theta)^2+a^2*r^2+r^4))/((r^2+a^2*cos(theta)^2)*(a^2-2*m*r+r^2))

 (3)

NULL

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