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Let's consider the following metric:

[tex]

g=dt^2 - a^2(t)\frac{dx^2+dy^2+dz^2}{1+\frac{x^2+y^2+z^2}{4}}

[/tex]

It can be also express in different coordinates as:

[tex]

g=dt^2 - a^2(t)\left( \frac{dr^2}{1-r^2} + r^2(\sin^2(\theta) d\varphi^2+\theta^2) \right)

[/tex]

Of course it admits killing vetctors which are generators of rotations:

[tex]

L_z=x\partial_y - y\partial_x, \ldots

[/tex]

Can anyone found different killing vector?

This metric describes spatialy homogenous universe so it should have

translation symmetry but it's not apparent in this coordinates.

Why it's hidden?

Thanks for any replies.

[tex]

g=dt^2 - a^2(t)\frac{dx^2+dy^2+dz^2}{1+\frac{x^2+y^2+z^2}{4}}

[/tex]

It can be also express in different coordinates as:

[tex]

g=dt^2 - a^2(t)\left( \frac{dr^2}{1-r^2} + r^2(\sin^2(\theta) d\varphi^2+\theta^2) \right)

[/tex]

Of course it admits killing vetctors which are generators of rotations:

[tex]

L_z=x\partial_y - y\partial_x, \ldots

[/tex]

Can anyone found different killing vector?

This metric describes spatialy homogenous universe so it should have

translation symmetry but it's not apparent in this coordinates.

Why it's hidden?

Thanks for any replies.

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