# Question on Weak Energy Condition

Hi,

I have just read that one of the restrictions on $$T^{\mu\nu}$$ is that:

$$T^{\mu\nu}u^au^b > 0$$

where u is a timelike vector.

Can someone please tell me WHAT u actually is (other than saying it is a timelike vector).

What sort of vector is it, what is the context???

i.e Once I have obtained the stress energy tensor and I want to test the weak energy condition then what u's to I multiply it by to see if it is greater than zero???

Thanks!

pervect
Staff Emeritus
robousy said:
Hi,

I have just read that one of the restrictions on $$T^{\mu\nu}$$ is that:

$$T^{\mu\nu}u^au^b > 0$$

where u is a timelike vector.

Can someone please tell me WHAT u actually is (other than saying it is a timelike vector).

What sort of vector is it, what is the context???

i.e Once I have obtained the stress energy tensor and I want to test the weak energy condition then what u's to I multiply it by to see if it is greater than zero???

Thanks!

u is the 4-velocity of a hypothetical observer. An observer can't have a space-like 4-vector, an observer must be moving slower than light. The above equation is thus telling you that the energy density must be positive for all observers, where an observer can have any 4-velocity as long as it's timelike.

aaah, ok thanks a lot.

That makes sense.