I know that already exist a question on "how to calculate 4-velocity components"$[1]$; the conclusion of the answers were that 4-velocity and the metric are quite unrelated concepts, concerning calculations of 4-velocity components.

Nervertheless, I would like to know if there's tricks and tips to calculate these components. For instance, it seems that the normalisation constrain:

$$ u_{\mu}u^{\mu} = -1 \tag{1}$$

plays an desicive role on how calculate 4-velocity components in an arbitrary spacetime. Furthermore, even though the metric appears just as an tensor operation:

$$ g_{\mu\nu}u^{\mu}u^{\nu} := u_{\mu}u^{\mu} = -1 \tag{2}$$

we have, still, a relationship between these two tensors.

So, I would like to ask:

If someone give me a metric tensor and ask: "what are the components of 4-velocity?" how can I calculate the components?

$$ * * * $$

$[1]$ How to get the four-velocity components from a given metric tensor?

I know that already exist a question on How to get the four-velocity components from a given metric tensor? the conclusion of the answers were that 4-velocity and the metric are quite unrelated concepts, concerning calculations of 4-velocity components.

Nevertheless, I would like to know if there's tricks and tips to calculate these components. For instance, it seems that the normalisation constrain:

$$ u_{\mu}u^{\mu} = -1 \tag{1}$$

plays an desicive role on how calculate 4-velocity components in an arbitrary spacetime. Furthermore, even though the metric appears just as an tensor operation:

$$ g_{\mu\nu}u^{\mu}u^{\nu} := u_{\mu}u^{\mu} = -1 \tag{2}$$

we have, still, a relationship between these two tensors.

So, I would like to ask:

If someone give me a metric tensor and ask: "what are the components of 4-velocity?" how can I calculate the components?

$$ * * * $$

$[1]$ How to get the four-velocity components from a given metric tensor?