Weak energy condition

The weak energy condition requires

T_{μν} X^{μ} X^{ν} \geq 0

for every timelike vector

X

, so every observer measures nonnegative energy density.

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- Weak energy condition for a quadratic scalar stress-energy ansatz Weak energy condition

Weak energy condition for a quadratic scalar stress-energy ansatz

For the general scalar ansatz in Conserved Klein-Gordon scalar stress-energy ansatz, work in a unit timelike frame. Then

2 T_{00} = (1 + A) (\partial_{0} ϕ)^{2} - A ∣ \nabla_{s} ϕ ∣^{2} - B ϕ^{2} .

The weak energy condition for arbitrary local field data is therefore equivalent to

- 1 \leq A \leq 0, B \leq 0.

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