标题： 从非定域源得到的超普朗克尺度下的半经典时空 显示英文标题

标题： Semiclassical spacetimes at super-Planckian scales from delocalized sources

摘要： 我们推导了由处于不同位置量子叠加态的源产生的引力场和时空度规。 我们首先在牛顿近似下进行研究，在此近似中，有效引力势被计算为源的位置在宽度为$R$的高斯分布下的引力势算符的期望值。 然后将有效引力势协变地提升为广义相对论中的完全相对论性度规，描述通过对这种源的状态进行平均来产生的时空。 通过采用基于量子参考系的独立构造，这些结果被重新推导并扩展。 我们发现三类量子有效度规，它们都是渐近平直的，并在远距离处重现施瓦茨希尔德度规。 然而，这些解在内部核心有所不同。 源位置的量子不确定性$\Delta r\sim R$阻止横向二维球面的半径收缩为零。 根据量子叠加效应的强度，我们得到要么是一个具有“量子毛发”和事件视界的无奇点黑洞，要么是一个具有临界光喉的一向虫洞，要么是一个可穿越虫洞。 我们还对这三种模型家族的时空结构的几何和热力学特性以及它们的物理现象进行了详细研究。 显示英文摘要

摘要： We derive the gravitational field and the spacetime metric generated by sources in quantum superposition of different locations. We start by working in a Newtonian approximation, in which the effective gravitational potential is computed as the expectation value of the gravitational potential operator in a Gaussian distribution of width $R$ for the position of the source. The effective gravitational potential is then covariantly uplifted to a fully relativistic metric in general relativity, describing the spacetime generated by averaging over the state of such sources. These results are then rederived and extended by adopting an independent construction in terms of quantum reference frames. We find three classes of quantum effective metrics which are all asymptotically flat and reproduce the Schwarzschild metric at great distances. The solutions differ, however, in the inner core. The quantum uncertainty $\Delta r\sim R$ in the position of the source prevents the radius of the transverse two-sphere to shrink to zero. Depending on the strength of the quantum superposition effects, we have either a nonsingular black hole with a ``quantum hair'' and an event horizon, a one-way wormhole with a critical null throat or a traversable wormhole. We also provide a detailed study of the geometric and thermodynamic properties of the spacetime structure for each of these three families of models, as well as their phenomenology.