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## Homework Statement

Calculate the lie derivative of the metric tensor, given the metric,

[itex]

g_{ab}=diag(-(1-\frac{2M}{r}),1-\frac{2M}{r},r^2,R^2sin^2\theta)

[/itex]

and coordinates (t,r,theta,phi)

given the vector

[itex]

E^i=\delta^t_0

[/itex]

## Homework Equations

[itex]

(L_Eg)ab=E^cd_cg_{ab}+g_{cb}d_aE^c+g_{ac}d_bE^c

[/itex]

## The Attempt at a Solution

[itex]

(L_Eg)ab=E^cd_cg_{ab}+g_{cb}d_aE^c+g_{ac}d_bE^c

[/itex]

all derivatives above being partial

Now the Last two terms go to zero, since E^i=Kronecker delta=constant and so its derivative is zero.

So,

[itex]

(L_Eg)ab=E^cd_cg_{ab}

[/itex]

[itex]

(L_Eg)ab=\delta^t_0 d_cg_{ab}

[/itex]

I'm unsure how to take it from here.

Firstly, I'm unsure what

[itex]

\delta^t_0

[/itex]

means. Does it means we get the result 1 at t=0 and zero for all other times?

How does it then affect the equation below.

[itex]

(L_Eg)ab=\delta^t_0 d_cg_{ab}

[/itex]

Please help.

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