黑洞的演化与量子信息的研究

Under Hawking evaporation, the mass of a black hole becomes smaller and smaller in time. However there remain a lot of interesting phenomena in the process of Hawking evaporation to be studied. In addition, these few years have witnessed the very interesting applications of quantum information theory in black hole physics. Among the important concepts are quantum entanglement entropy and quantum complexity. The former is crucial in the discussion of black hole information loss, while the latter is a new topic, which is related to the interior volume of a black hole. In order to understand whether information is lost in a black hole, it is important to understand the entire process of Hawking evaporation, as well as the evolution of the corresponding quantum entanglement entropy and quantum complexity. In the literature, research on black hole evolution is still mostly focused on asymptotically flat spacetimes. However, black hole physics is much richer and interesting in asymptotically AdS spacetimes, which also allows one to study strongly coupled quantum field theory via AdS/CFT (holography) correspondence. In our investigations, we plan to.(1).Solve the evolution of various AdS black holes under Hawking evaporation via numerical methods, and analyse the time scale of the evolution to compare with various important time scales in quantum information theory, such as the decoding time scale..(2).Further investigate black hole volume and its relationship with quantum complexity..(3).Study Hawking evaporation via 2-dimensional moving mirrors. Such an “analogue black hole” allows explicit and more rigorous calculations, and potentially can be linked with experiments.

黑洞在霍金蒸发的过程中质量会越来越小，但是整个蒸发过程有很多有趣的现象值得研究。另外，近年来，量子信息理论被应用到黑洞物理上，其中重要的概念是量子纠缠熵和量子复杂度。前者在黑洞信息遗失悖论中扮演不可或缺的角色，而后者仍是新颖的课题，与黑洞的体积有关。要了解黑洞信息是否遗失，了解整个蒸发过程以及相关的量子纠缠熵和量子复杂度如何演化将是非常重要的。有关黑洞演化这方面的研究文献上主要还是注重于渐进平直时空，但是黑洞物理在渐进AdS的时空中更为丰富有趣，也可以通过AdS/CFT全息对偶去研究与之对应的强耦合场论。本项目中，我们主要将研究AdS黑洞的演化，具体研究内容包括：.(1)通过数值方法解AdS各种黑洞在霍金辐射下的演化，并分析演化的时间尺度，和量子解码等时间尺度做比较。.(2)进一步研究各种黑洞的体积与其和量子复杂度的关系。.(3)通过研究二维时空的镜子运动模拟黑洞霍金蒸发。

黑洞在霍金蒸发的过程中质量会越来越小，但是整个蒸发过程有很多有趣的现象值得研究。另外，近年来，量子信息理论被应用到黑洞物理上，其中重要的概念是量子纠缠熵和量子复杂度。前者在黑洞信息遗失悖论中扮演不可或缺的角色，而后者仍是新颖的课题，与黑洞的体积有关。本项目对黑洞热力学、霍金蒸发演化的过程以及黑洞体积、量子复杂度等课题进行了研究，证实了Kerr-AdS黑洞的体积满足复杂度=体积的CV猜想。..本项目也探讨了黑洞在蒸发的过程中是否有可能违反宇宙监督猜想，发现dilaton耦合的带电黑洞在霍金辐射演化下，要求宇宙监督猜想成立的话，可以反推处正确的带电粒子产生率，后者可以通过场论独立检验。为宇宙监督猜想在霍金蒸发下成立提供有力证据。..有关黑洞演化这方面的研究文献上主要还是注重于渐进平直时空，但是黑洞物理在渐进AdS的时空中更为丰富有趣，也可以通过AdS/CFT全息对偶去研究与之对应的强耦合场论。有鉴于此，本项目中，我们也研究了各种引力理论与量子修正后的AdS黑洞的演化，尤其注重在黑洞是否能在有限时间内完全蒸发或形成残骸。.本项目也通过研究二维时空的镜子运动模拟黑洞霍金蒸发，探讨量子信息如何保持幺正演化的问题。