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

在黑洞形成期间和之后发生的与微观（量子）效应有关的现象将被研究。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，并可能提供关于黑洞如何形成的信息发生了什么的重要问题的见解。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具有正确配置的特性，那么量子效应就会发生，在某些重要的方面类似于发生在黑洞中的那些。不同之处在于，玻色-爱因斯坦凝聚体可以在实验室中进行研究。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效应。一个重要的近似称为半经典近似的有效性，它被用作宏观（经典）和微观（量子）现象之间的桥梁，将在两种情况下进行研究。一个是粒子产生对宇宙动力学的影响，这是一个重要的模型，在这个模型中，宇宙从收缩开始，然后膨胀。另一个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训练，并共同撰写出版物。提出的研究将调查与黑洞如何形成的信息有关的问题；模拟黑洞系统中量子效应的存在与视界的存在有关，这可以在实验室研究中观察到；半经典近似的有效性在某些情况下，量子效应是显著的。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，调查在引力坍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。对于玻色-爱因斯坦凝聚体（可以作为黑洞的类似物），目标是确定是否会出现需要视界存在的波动或其他新的可观测效应。半经典近似的有效性将研究一个重要的模型（德西特空间），其中收缩是最小的尺寸，然后是膨胀。将在黑洞和宇宙学研究中对量子场的应力能进行数值计算，在宇宙学的情况下，将计算时空几何上的反作用。

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.