Lorentzian wormholes in higher-derivative gravity and the weak energy condition.

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The possibility of the existence of a traversible wormhole solution which does not break the weak energy condition is examined in a higher-derivative theory of gravity. No such solution is found, suggesting that a Lorentzian wormhole without the violation of the weak energy condition is incompatible with a wide class of gravitational theories. We show this in two simple examples of spherically symmetric wormhole solutions.