On the observer dependence of the Hilbert space near the horizon of black holes
On the observer dependence of the Hilbert space near the horizon of black holes
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DOI：
10.1093/ptep/pty146
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发表时间：
2018-03
影响因子：
3.5
通讯作者：
Kanato Goto;Y. Kazama
中科院分区：
文献类型：
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作者：
Kanato Goto;Y. Kazama
与其他相互作用不同，引力的显着特征之一是，不存在独立于时空坐标选择的局部可观测量。这一性质在量子领域中具有至关重要的意义，因为与不同观察者相关的希尔伯特空间的结构可能截然不同。霍金辐射、安鲁效应等令人好奇的现象都源于这一特征。正如在这些例子中一样，由于这种观察者依赖性而产生的量子效应在事件视界存在时最为明显，并且在这种情况下仍然有许多问题需要澄清。在本文中，我们对史瓦西黑洞视界附近四个维度的无质量标量场的量子希尔伯特空间的观察者依赖性进行了全面而明确的研究，无论是在永恒（两侧）情况下还是在由物质塌缩产生的物理（一侧）情况下。具体来说，我们比较并关联了三种类型观察者的希尔伯特空间，即（i）自由落体观察者，（ii）停留在地平线外固定适当距离的观察者和（iii）从外部连续分析的地平线内部的自然观察者。我们获得的具体结果对于与量子等效原理和相关防火墙现象有关的黑洞互补性、每种类型观察者看到的自由度数以及在纯态下实现的粒子的“热型”光谱有许多重要的影响。
One of the pronounced characteristics of gravity, distinct from other interactions, is that there are no local observables which are independent of the choice of the spacetime coordinates. This property acquires crucial importance in the quantum domain in that the structure of the Hilbert space pertinent to different observers can be drastically different. Such intriguing phenomena as the Hawking radiation and the Unruh effect are all rooted in this feature. As in these examples, the quantum effect due to such observer-dependence is most conspicuous in the presence of an event horizon and there are still many questions to be clarified in such a situation. In this paper, we perform a comprehensive and explicit study of the observer dependence of the quantum Hilbert space of a massless scalar field in the vicinity of the horizon of the Schwarzschild black holes in four dimensions, both in the eternal (two-sided) case and in the physical (one-sided) case created by collapsing matter. Specifically, we compare and relate the Hilbert spaces of the three types of observers, namely (i) the freely falling observer, (ii) the observer who stays at a fixed proper distance outside of the horizon and (iii) the natural observer inside of the horizon analytically continued from outside. The concrete results we obtain have a number of important implications on black hole complementarity pertinent to the quantum equivalence principle and the related firewall phenomenon, on the number of degrees of freedom seen by each type of observer, and on the "thermal-type" spectrum of particles realized in a pure state.