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I want to prove (or disprove) that the vector with components

[tex]\xi^u = \frac{v}{2 r_s}\hspace{5 mm} \xi^v = \frac{u}{2 r_s}[/tex]

is a Killing vector of the KS space-time with line element

[tex]\frac{4 r_s^3}{r} e^{-\frac{r}{r_s}} \left( du^2 -dv^2\right) + r^2 \left( d\theta^2 + sin^2 \theta d\phi^2\right) [/tex]

Here r is an implicit function of u,v, which is handled by a constraint equation.

However, I seem to be having a hard time getting GRT to handle the contraints. I try

[tex]\left( \frac{r}{r_s} - 1 \right) e^{\frac{r}{r_s}} = u^2 - v^2[/tex] directly, but it doesn't simplify.

I try to feed it the following

[tex]

{\frac {\partial }{\partial u}}r \left( u,v \right) =2\,{{\it r\_s}}^{

2}u \left( r \left( u,v \right) \right) ^{-1} \left( {e^{{\frac {r

\left( u,v \right) }{{\it r\_s}}}}} \right) ^{-1}

[/tex]

but it complains about "illegal use of object as a name", I can't see what it's objecting to.

So a) -does this look like the right expression for the Killing Vector? And b) - how does one successfully get the constraints into GrTensor?

[tex]\xi^u = \frac{v}{2 r_s}\hspace{5 mm} \xi^v = \frac{u}{2 r_s}[/tex]

is a Killing vector of the KS space-time with line element

[tex]\frac{4 r_s^3}{r} e^{-\frac{r}{r_s}} \left( du^2 -dv^2\right) + r^2 \left( d\theta^2 + sin^2 \theta d\phi^2\right) [/tex]

Here r is an implicit function of u,v, which is handled by a constraint equation.

However, I seem to be having a hard time getting GRT to handle the contraints. I try

[tex]\left( \frac{r}{r_s} - 1 \right) e^{\frac{r}{r_s}} = u^2 - v^2[/tex] directly, but it doesn't simplify.

I try to feed it the following

[tex]

{\frac {\partial }{\partial u}}r \left( u,v \right) =2\,{{\it r\_s}}^{

2}u \left( r \left( u,v \right) \right) ^{-1} \left( {e^{{\frac {r

\left( u,v \right) }{{\it r\_s}}}}} \right) ^{-1}

[/tex]

but it complains about "illegal use of object as a name", I can't see what it's objecting to.

So a) -does this look like the right expression for the Killing Vector? And b) - how does one successfully get the constraints into GrTensor?

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