论文标题
动量/复杂度对应的证明
Proof of a Momentum/Complexity Correspondence
论文作者
论文摘要
我们表明，基于一般相对论的动量约束，全息复杂性=体积提议满足了动量/复杂性对应（PC）的一般概念。它将复杂性变化的速率与适当的物质动量通量联系起来，使得通过空隙为极端表面。这正式表明了物质的“引力堵塞”会增加复杂性，并且表明“插入动量”的所需概念具有表达这一想法的牛顿头像。发现PC对应关系的所提出的形式对于在2+1个维的Einstein方程的任何解决方案中都是准确的，并且在任意维度中的任何球形对称溶液都使用球形薄壳概括了所有先前的计算。重力辐射通过校正进入，该校正没有直接解释为PC对应关系。精确PC二元性的其他障碍物具有拓扑来源，并在存在虫洞的情况下出现。
We show that the holographic Complexity = Volume proposal satisfies a very general notion of Momentum/Complexity correspondence (PC), based on the Momentum Constraint of General Relativity. It relates the rate of complexity variation with an appropriate matter momentum flux through spacelike extremal surfaces. This formalizes the intuitive idea that `gravitational clumpling' of matter increases complexity, and the required notion of `infall momentum' is shown to have a Newtonian avatar which expresses this idea. The proposed form of the PC correspondence is found to be exact for any solution of Einstein's equations in 2+1 dimensions, and any spherically symmetric solution in arbitrary dimensions, generalizing all previous calculations using spherical thin shells. Gravitational radiation enters through a correction which does not have a straightforward interpretation as a PC correspondence. Other obstructions to an exact PC duality have a topological origin and arise in the presence of wormholes.
