盒中Kruskal黑洞和1+1 Minkowski时空中匀加速镜下无质量场的等距不变Hadamard态的不存在性
Non-existence of isometry-invariant Hadamard states for a Kruskal black hole in a box and for massless fields on 1+1 Minkowski spacetime with a uniformly accelerating mirror
摘要：
我们猜想（当阿达玛态的概念被适当地采用时），对于定义在右史瓦西楔形中的常数史瓦西半径的表面左边的Kruskal时空区域上的有质量或无质量协变Klein-Gordon方程，当Dirichlet边界条件放在该表面上时，不存在等距不变的阿达玛态。我们还证明了，通过适当定义“升压不变Hadamard态”（我们称之为“强助推不变的全球阿达玛”），它既考虑了类时边界的存在和特殊的无质量1+1红外病理学，在1+1闵可夫斯基空间的区域上，在一个永远均匀加速的镜子的左边，无质量的波动方程不存在这样的状态--Dirichlet边界条件这个结果是重要的，因为如果在左楔中也有一个对称放置的减速反射镜（并且排除该反射镜左侧的区域），则这种状态确实存在。我们期望一个类似的存在结果，以保持Kruskal时，有对称放置的球形盒在右和左史瓦西楔。我们的Kruskal no-go猜想提出了关于在黑洞热力学中考虑的盒子中的黑洞的基本问题。如果是真的，它将进一步支持B. S.凯'封闭地平线的不稳定性'，将军Rel。重力47，1-27（2015）（arXiv：1310.7395），对于经典时空来说，最接近于描述盒子中处于平衡状态的黑洞的东西是外史瓦西解，经典时空图像在视界附近破裂。附录指出存在的，并部分填补了空白的证明定理在BS。凯和R. M. Wald Phys.Rep.207，49-136（1991）。
英文摘要：
We conjecture that (when the notion of Hadamard state is suitably adapted) there is no isometry-invariant Hadamard state for the massive or massless covariant Klein-Gordon equation defined on the region of the Kruskal spacetime to the left of a surface of constant Schwarzschild radius in the right Schwarzschild wedge when Dirichlet boundary conditions are put on that surface. We also prove that, with a suitable definition for 'boost-invariant Hadamard state' (which we call 'strongly boost-invariant globally-Hadamard') which takes into account both the existence of the timelike boundary and the special massless 1+1 infra-red pathology, there is no such state for the massless wave equation on the region of 1+1 Minkowski space to the left of an eternally uniformly accelerating mirror -- with Dirichlet boundary conditions. This result is significant because such a state does exist if there is also a symmetrically placed decelerating mirror in the left wedge (and the region to the left of this mirror is excluded). We expect a similar existence result to hold for Kruskal when there are symmetrically placed spherical boxes in both right and left Schwarzschild wedges. Our Kruskal no-go conjecture raises basic questions about the black holes in boxes considered in black hole thermodynamics. If true, it would lend further support to the conclusion of B.S. Kay 'Instability of enclosed horizons', Gen. Rel. Grav. 47, 1-27 (2015) (arXiv: 1310.7395) that the nearest thing to a description of a black hole in equilibrium in a box in terms of a classical spacetime with quantum fields propagating on it has, for the classical spacetime, the exterior Schwarzschild solution, with the classical spacetime picture breaking down near the horizon. An appendix points out the existence of, and partially fills, a gap in the proofs of the theorems in B.S. Kay and R.M. Wald Phys. Rep. 207, 49-136 (1991).
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