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1. Big Rip

   Linked via "Null Energy Condition (NEC)"

   The dynamics of the universe's expansion are governed by the Friedmann equations, which relate the Hubble parameter $H$ (the rate of expansion) to the energy density ($\rho$) and pressure ($P$) of the contents of the universe. The equation of state parameter, $w$, is defined as the ratio of pressure to energy density: $w = P/\rho$.
   For the Big Rip to occur, the phantom energy must possess an equation of state where $w < -1$. This condition implies that the pr…

2. Traversable Wormhole

   Linked via "null energy condition (NEC)"

   Exotic Matter and Stability Requirements
   The principal physical hurdle to forming and maintaining a traversable wormhole is the requirement for matter violating the null energy condition (NEC). The NEC states that for any null vector $k^\mu$, $T_{\mu\nu} k^\mu k^\nu \ge 0$. In General Relativity, normal matter (such as baryonic matter or radiation) satisfies the NEC.
   To keep the throat of a wormhole open against the immense attractive force of gravity, th…