Studies Relating to Black Hole Evaporation and to the Validity of the Semiclassical Approximation in Cosmology

该奖项支持对黑洞蒸发过程的研究，重点是研究黑洞形成期间和之后的量子效应。这些结果可能会让我们深入了解关于黑洞如何形成的信息会发生什么这一重要问题。玻色-爱因斯坦凝聚体是典型的含有非常冷的原子的系统。对于某些构型，量子效应会发生，在某些重要方面与黑洞的量子效应相似。对玻色-爱因斯坦凝聚类黑洞进行了实验研究。理论计算将使用与研究与真实黑洞相关的量子效应相同的技术。将计算结果与实验数据进行比较。半经典近似已被用于研究各种情况下的量子效应，例如粒子的产生，包括早期宇宙。它在宏观(经典)和微观(量子)现象之间架起了一座桥梁。它的有效性将被用来研究一个重要的模型，在这个模型中，宇宙最初收缩，达到最小尺寸，然后开始膨胀。预计粒子生产在收缩阶段将特别重要，在这个阶段，粒子生产可能会显著改变宇宙的动态演化。这些结果将有助于确定半经典近似在量子效应显著的情况下是否有效。四名研究生，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。结果将通过出版物和在国家和国际会议上的介绍向研究界传播。获得的一些结果将与凝聚态物理相关。这笔拨款支持的研究涉及黑洞蒸发、可用作黑洞类比的玻色-爱因斯坦凝聚体中的可观测效应，以及早期宇宙宇宙学。具体地说，它将调查与黑洞如何形成的信息有关的问题，与模拟黑洞系统中量子效应相关的理论和实验结果之间的一致性，以及半经典近似在宇宙模型中的有效性。在黑洞蒸发的情况下，目标包括详细研究球对称零壳坍塌形成黑洞时发生的量子效应。其中一个目标是检查二维引力膨胀理论中类似计算的准确性。也有可能洞察到关于黑洞是如何形成的信息会发生什么的问题。可以用作模拟黑洞的玻色-爱因斯坦凝聚体已经在实验室中被创造出来。其目的是确定某些实验结果是否与量子场理论在模拟时空中的弯曲空间计算中得出的预测是定量一致的。宇宙学的主要目标是确定半经典近似对于宇宙收缩到最小尺寸然后膨胀的模型是否有效。所使用的模型将由一个具有正宇宙常数的封闭宇宙组成。对于黑洞蒸发计划，在空壳坍塌形成黑洞的情况下，量子化的无质量最小耦合标量场的应力-能量张量将在四维中进行数值计算。对于宇宙学计划，在质量共形耦合标量场存在的情况下，半经典反反应方程将被数值求解。这些结果将被用来研究半经典近似在塌缩宇宙中的有效性。模拟玻色-爱因斯坦凝聚态黑洞的密度密度关联函数将使用弯曲空间技术中的量子场论计算，模型的速度和声速曲线与实验中使用的速度和声速曲线非常匹配。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports studies on black hole evaporation processes, with a focus on investigating quantum effects during and after the formation of a black hole. The results may provide insight into the important question of what happens to the information about how a black hole forms. Bose-Einstein condensates are systems that typically contain very cold atoms. For certain configurations, quantum effects will occur which are in some important ways similar to those that occur for black holes. Experimental studies of Bose-Einstein condensate analog black holes have been carried out. Theoretical calculations will be made using the same techniques as are used to study quantum effects related to real black holes. The results will be compared with the experimental data. The semiclassical approximation has been used to investigate quantum effects such as particle production in a variety of situations including the early universe. It provides a bridge between macroscopic (classical) and microscopic (quantum) phenomena. It's validity will be studied for an important model in which the universe is initially contracting, reaches a minimum size, and then begins to expand. Particle production is expected to be particularly important during the contracting phase where it could significantly alter the dynamical evolution of the universe. The results will help to determine whether the semiclassical approximation is valid in cases where quantum effects are significant. Four 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. Results will be disseminated to the research community through publications and presentations at national and international meetings. Some results obtained will be relevant for condensed matter physics.The research supported by this grant addresses black hole evaporation, observable effects in Bose-Einstein condensates which can serve as black hole analogs, and early universe cosmology. Specifically, it will investigate questions related to the information about how a black hole forms, the correspondence between theoretical and experimental results related to quantum effects in analog black hole systems, and the validity of the semi-classical approximation in models of the universe. In the case of black hole evaporation, the objectives include studying in detail quantum effects that occur if a spherically symmetric null shell collapses to form a black hole. One goal is to check the accuracy of similar calculations in two dimensional dilaton theories of gravity. It is also possible that insight will be gained into the question of what happens to the information about how the black hole formed. Bose-Einstein condensates that can serve as analog black holes have been created in the laboratory. The goal is to determine whether certain experimental results are in quantitative agreement with predictions resulting from quantum field theory in curved space calculations in the analog spacetime. The primary goal for cosmology is to determine whether the semiclassical approximation is valid for models in which the universe contracts to a minimum size and then expands. The models used will consist of a closed universe with a positive cosmological constant. For the black hole evaporation project the stress-energy tensor for a quantized massless minimally coupled scalar field will be numerically computed in four-dimensions in the case of a null shell that collapses to form the black hole. For the cosmology project the semiclassical backreaction equations will be solved numerically in the case that a massive conformally coupled scalar field is present. The results will be used to investigate the validity of the semiclassical approximation in a collapsing universe. The density density correlation function for a Bose-Einstein condensate analog black hole will be computed using quantum field theory in curved space techniques for a model that closely matches the velocity and sound speed profiles used in the experiments.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.