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。这些结果可能会对一个重要的问题提供见解，即关于黑洞如何形成的信息发生了什么。玻色-爱因斯坦凝聚体通常包含非常冷的原子。对于某些构型，量子效应会发生，在一些重要的方面类似于发生在黑洞中的量子效应。对玻色-爱因斯坦凝聚模拟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。计算结果将与实验数据进行比较。半经典近似已被用于研究量子效应，如在各种情况下的粒子产生，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。它的有效性将在一个重要的模型中得到研究，在这个模型中，宇宙最初收缩，达到最小尺寸，然后开始膨胀。粒子的产生预计在收缩阶段特别重要，因为它可以显著地改变宇宙的动态演化。结果将有助于确定在量子效应显著的情况下，半经典近似是否有效。四名研究生，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。研究结果将通过出版物和在国家和国际会议上的发言向研究界传播。所得的一些结果将与凝聚态物理有关。该基金支持的研究涉及黑洞蒸发、玻色-爱因斯坦凝聚物（可以作为黑洞类似物）的可观测效应以及早期宇宙宇宙学。具体来说，它将研究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对应关系，以及宇宙模型中半经典近似的有效性。在黑洞蒸发的情况下，目标包括详细研究如果球对称的零壳坍塌形成黑洞所发生的量子效应。其中一个目标是检验二维引力膨胀理论中类似计算的准确性。也有可能对黑洞如何形成的信息发生了什么问题有所了解。可以作为模拟黑洞的玻色-爱因斯坦凝聚体已经在实验室中被创造出来。目标是确定某些实验结果是否与模拟时空中弯曲空间计算中量子场论的预测在定量上一致。宇宙学的主要目标是确定半经典近似是否对宇宙收缩到最小尺寸然后膨胀的模型有效。所使用的模型将包括一个具有正宇宙常数的封闭宇宙。对于黑洞蒸发项目，将在四维空间中对零壳坍缩形成黑洞的情况下量子化无质量最小耦合标量场的应力-能量张量进行数值计算。对于宇宙学项目，在存在大量共形耦合标量场的情况下，将对半经典反反应方程进行数值求解。这些结果将用于研究在坍缩宇宙中半经典近似的有效性。玻色-爱因斯坦凝聚模拟黑洞的密度相关函数将使用弯曲空间技术中的量子场理论计算，该模型与实验中使用的速度和声速剖面密切匹配。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.