We investigate possible manifolds characterizing traversable wormholes in the presence of a scalar field minimally coupled to gravity, which has both kinetic and potential energy. The feature of traversability requires the violation of the null energy condition, which, in turn, signals the existence of exotic matter with negative energy density. To achieve this, we introduce a hypothetical Casimir apparatus with plates positioned either at a parametrically fixed or radially varying distance. A consistent set of field equations requires the introduction of an auxiliary field composed solely of pressure terms, which we interpret as the gravitational back-reaction of the traversable wormhole to the original source. Interestingly, the only case that appears to avoid the need for such an auxiliary field involves a scalar field with potential energy, combined with a Casimir device with fixed plates.

中文翻译：

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应力能量守恒诱导的可穿越虫洞：将卡西米尔能量与标量场相结合


我们研究了在与重力最小耦合的标量场存在的情况下表征可穿越虫洞的可能流形，该标量场同时具有动能和势能。可遍历性的特征需要违反零能量条件，这反过来又表明存在具有负能量密度的奇异物质。为了实现这一点，我们引入了一个假设的 Casimir 装置，其板位于参数固定或径向变化的距离。一组一致的场方程需要引入一个仅由压力项组成的辅助场，我们将其解释为可穿越虫洞对原始源的引力反向反应。有趣的是，似乎唯一避免需要这种辅助场的情况是具有势能的标量场，并结合了带有固定板的 Casimir 装置。