# Null energy condition (NEC) The null energy condition states that $T_{ab}V^aV^b\ge 0$ for any null vector $V^a$, where $T_{ab}$ is the stress tensor. By Einstein's equation, it translates to $R_{ab}V^aV^b\ge 0$, where $R_{ab}$ is the Ricci tensor. It is often needed to ensure certain properties of the spacetime or to avoid pathological ones. It can be violated with quantum fields, in which case it is usually replaced by other [[0247 Energy conditions|energy conditions]] such as the achronal [[0417 Averaged null energy condition|averaged null energy condition]] (AANEC). This allows more interesting things to appear such as the [[0083 Traversable wormhole|traversable wormhole]], which is forbidden by NEC. In [[0001 AdS-CFT|holography]], one often requires AANEC at each order in the perturbative expansion in $1/N\sim G_N\hbar$, which reduces to NEC at leading order. ## Implications or things that need it - non-[[0115 Superluminality|superluminality]] - [[0091 Boundary causality|boundary causality]] - [[0142 Entanglement wedge nesting|entanglement wedge nesting]] - no [[0083 Traversable wormhole|traversable wormholes]] - [[0225 Singularity theorems|singularity theorems]] - two types of flows both pass through the [[0007 RT surface|HRT]] surface (see [[HeadrickHubeny2022]]) - focusing theorem ([[0408 Raychaudhuri equation|Raychaudhuri equations]]) - the conditions of [[2020#Berenstein, Grabovsky]] - [[0350 Holographic c-theorem|holographic c-theorem]] - [[0005 Black hole second law|BH second law]]