Quantum Effects for Black Holes and Analog Black Holes and the Validity of the Semiclassical Approximation

本课程将研究与黑洞形成期间和之后发生的微观(量子)效应有关的现象。这些结果将检验使用黑洞存在于一个空间维度的简单模型所做的预测，并可能提供对有关黑洞如何形成的信息发生什么这一重要问题的洞察。如果一个被称为玻色-爱因斯坦凝聚体的非常冷的原子系统的性质配置正确，那么量子效应就会发生，这种效应在某些重要方面类似于黑洞的效应。不同的是，玻色-爱因斯坦凝聚体可以在实验室进行研究。将对这类系统进行调查，目的是预测在实验室中可以观察到的影响。作为宏观(经典)和微观(量子)现象之间的桥梁的半经典近似的有效性将在两种情况下进行研究。一个是粒子生产对宇宙动力学的影响，在这个重要模型中，宇宙从收缩开始，然后膨胀。另一类是关于粒子产生对强电场的影响。一名或多名研究生，可能还有一些本科生，将参与这项研究的某些方面，继续他们在数值和分析研究技术方面的长期培训，以及在出版物方面的合作。拟议的研究将调查与以下信息有关的问题：黑洞是如何形成的；模拟黑洞系统中与视界存在相关的量子效应的存在，这可以在实验室研究中观察到；以及在量子效应显著的某些情况下，半经典近似的有效性。在黑洞蒸发的情况下，目标包括确定量子效应在黑洞内部的重要性，并调查引力塌缩形成黑洞期间外部区域粒子产生的细节，以便深入了解关于黑洞如何形成的信息发生了什么问题，并检查二维引力膨胀理论中类似计算的准确性。对于可以作为黑洞类似物的玻色-爱因斯坦凝聚体，目标是确定是否会预测到需要视界存在的波动或其他新的可观察到的效应。对于一个重要的模型(De Sitter空间)，我们将研究半经典近似的有效性，在该模型中，收缩到最小尺寸，然后是展开。在黑洞和宇宙学研究中，将对量子场的应力-能量进行数值计算，在宇宙学情况下，将计算时空几何上的反向反应。

Phenomena relating to microscopic (quantum) effects which occur during and after the formation of a black hole will be studied. The results will test predictions made using simple models in which the black hole exists in one space dimension and may provide insight into the important question of what happens to the information about how a black hole forms. If a system of very cold atoms called a Bose-Einstein condensate has its properties configured correctly, then quantum effects will occur which are in some important ways similar to those which occur for black holes. The difference is that Bose-Einstein condensates can be studied in the laboratory. An investigation of such systems will be made with the goal of making predictions for effects that could be observed in the laboratory. The validity of an important approximation called the semiclassical approximation that is used as a bridge between macroscopic (classical) and microscopic (quantum) phenomena will be studied in two cases. One is the effect of particle production on the dynamics of the universe for an important model in which the universe begins by contracting and later expands. The other is for the effect of particle production on a strong electric field. One or more graduate students and probably some undergraduates will participate in some aspects of the research, continuing a long history of their training in numerical and analytical research techniques and co-authorship on publications. The research proposed will investigate questions related to the information about how a black hole forms; the existence of quantum effects in analog black hole systems related to the existence of a horizon, which can be observed in laboratory studies; and the validity of the semi-classical approximation in certain cases where quantum effects are significant. In the case of black hole evaporation the objectives include determining the importance of quantum effects in the interior of a black hole and investigating the details of particle production in the exterior region during gravitational collapse to form a black hole, in order to gain insight into the question of what happens to the information about how a black hole forms and to check the accuracy of similar calculations in two dimensional dilaton theories of gravity. For Bose-Einstein condensates, which can serve as analogs for black holes, the goal is to determine whether undulations or other new observable effects that require the existence of a horizon are predicted to occur. The validity of the semiclassical approximation will be studied for one important model (de Sitter space) in which the contraction is to a minimum size and is followed by an expansion. Numerical computations of the stress-energy of quantum fields will be made in the black hole and cosmological investigations and in the cosmological case the backreaction on the spacetime geometry will be computed.