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

将研究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。 结果将测试使用简单模型做出的预测，其中黑洞存在于一个空间维度中，并可能深入了解有关黑洞如何形成的信息会发生什么的重要问题。 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的性质配置，那么就会发生量子效应，这在某些重要方面与黑洞发生的量子效应相似。 不同的是，玻色-爱因斯坦凝聚可以在实验室中进行研究。 将对这种系统进行调查，目的是预测在实验室中可以观察到的影响。一个重要的近似称为半经典近似，被用作宏观（经典）和微观（量子）现象之间的桥梁的有效性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，在一个重要的模型中，宇宙开始收缩，后来膨胀。 另一个是强电场对粒子产生的影响。 一个或多个研究生，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培训，并共同撰写出版物。拟议的研究将调查与黑洞如何形成的信息有关的问题;在与视界存在有关的模拟黑洞系统中存在量子效应，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，目标包括确定黑洞内部量子效应的重要性，并调查引力坍缩形成黑洞期间外部区域粒子产生的细节，为了深入了解黑洞如何形成的信息发生了什么变化，并检查二维宇宙中类似计算的准确性，引力理论 对于玻色-爱因斯坦凝聚，它可以作为黑洞的类似物，目标是确定是否预测会发生波动或其他需要视界存在的新的可观察效应。 半经典近似的有效性将研究一个重要的模型（德西特空间），其中的收缩是一个最小的尺寸，其次是一个扩展。 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.