Null Energy Condition: What Is It?

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The null energy condition (NEC) is a principle in theoretical physics defined by the inequality T_{\mu \nu} A^{\mu} A^{\nu} ≥ 0, where A is a null vector. It is often referenced in discussions about wormholes and indicates that for a perfect fluid, the condition translates to the requirement that the sum of energy density (ρ) and pressure (p) must be non-negative (ρ + p ≥ 0). Violating the NEC suggests a potential breach of the dominant energy condition (DEC), which could lead to phenomena such as faster-than-light effects. The implications of NEC violations are significant in the context of general relativity and exotic matter. Understanding these conditions is crucial for exploring theoretical constructs like wormholes.
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What is null energy condition?
I'm not sure whether this is the right forum to post but I come across this word when reading article about wormholes.
 
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The null energy condition means that:

T_{\mu \nu} A^{\mu} A^{\nu} \geq 0

With A a null vector. For a perfect fluid, it can be proven that this implies:

\rho + p \geq 0

I think that for \inline{\rho > 0}, the violation of the NEC is equivalent to a violation of the DEC (dominant energy condition). A perfect fluid that violates the DEC has faster than light effects, see https://www.physicsforums.com/showthread.php?t=78361
 

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