Studies of Classical and Quantum Effects in Gravity

该奖项支持几个涉及研究量子效应的项目，因为它们与宇宙学和黑洞有关。 同样的技术将被用来计算粒子在绕黑洞运行时由于引力辐射而感受到的力。 宇宙学中最重要的观点之一是，在宇宙历史的早期，宇宙经历了一个被称为暴胀的极其快速的膨胀过程。在暴胀期间和之后不久，量子效应都非常重要。 它们几乎总是用量子场论的一种近似来计算，称为半经典近似。 这个近似的有效性，因为它涉及到通货膨胀时期和粒子生产后，立即发生这一时期将被调查。 此外，还将研究量子场对黑洞视界的影响。 事件视界是光可以离开黑洞和不能离开黑洞之间的空间边界。 还将研究量子场对远离黑洞事件视界的几何形状的影响与它们对远离静态星星表面的几何形状的影响之间的差异。 当一个粒子围绕黑洞运行时，会发出引力辐射，其影响可以改变随后的轨道。 如果粒子带电，电磁辐射也会发射出来。这些可以通过使用称为标量辐射的更简单类型的辐射来建模。我们将致力于计算标量辐射在粒子绕黑洞运行时对粒子施加的力。一些最重要的暴胀预测，包括最终演化成星系的密度波动的产生，都依赖于量子效应，而量子效应是用半经典近似计算的。因此，确定这些近似值是否在通货膨胀期间和之后立即有效是极其重要的。 如果在某些混乱的通货膨胀情景中重新加热的计算是无效的，那么就需要更困难的计算。在黑洞的例子中，有迹象表明，在某些特殊情况下，量子效应可能对黑洞的事件视界产生如此显著的影响，以至于它们阻止了这种类型的黑洞的存在。 目前尚不清楚这种情况发生的可能性有多大，但重要的是要调查它是否会发生。 对于被称为丽莎的拟议中的天基引力波探测器来说，引力波的重要来源之一是中子星星或黑洞，它们是由一颗星星坍缩形成的，该恒星围绕星系中心的超大质量黑洞运行。 发射的波的具体性质取决于轨道物体的轨道。 这反过来又取决于发射的引力辐射对轨道物体的作用力。 因此，计算这个力是非常重要的。 这将是可能的，涉及本科生和研究生在许多这些项目。 有沿着历史的本科生和研究生从事这些类型的项目，并获得培训的数值和分析研究技术，以及共同作者的出版物。

This award supports several projects which involve studying quantum effects as they relate to both cosmology and black holes. The same techniques will be used to compute the force a particle feels due to the gravitational radiation that is emitted as it orbits a black hole. One of the most important ideas in cosmology today is that early in its history the universe underwent a process of extremely rapid expansion called inflation. Quantum effects were very important both during and shortly after this period of inflation. They are almost always computed using an approximation to quantum field theory called the semiclassical approximation. The validity of this approximation as it relates to the period of inflation and to particle production that occurs immediately after this period will be investigated. In addition, studies will be made of the effects that quantum fields have on the event horizons of black holes. The event horizon is the boundary in space between where light can get away from the black hole and where it cannot. A study will also be made of the difference between the effects quantum fields have on the geometry far from the event horizon of a black hole versus the effects they have on the geometry far from the surface of a static star. When a particle orbits a black hole gravitational radiation is emitted whose effect can change the subsequent orbit. If the particle is charged electromagnetic radiation is also emitted. These can be modeled by using a simpler type of radiation called scalar radiation. Projects will be worked on that involve the computation of the force this scalar radiation exerts on a particle as it orbits a black hole.Some of the most important predictions of inflation including the creation of density fluctuations that eventually evolve into galaxies depend on quantum effects which are computed using semiclassical approximations. It is thus extremely important to determine whether these approximations are valid both during and immediately after inflation. If calculations for reheating in some chaotic inflation scenarios are invalidated, then much more difficult calculations will be necessary. In the case of black holes there are indications that there are special cases where it is possible that quantum effects might have such a significant effect on the event horizon of the black hole that they prevent that type of black hole from existing. It is not clear how likely it is that this will happen but it is important to investigate whether or not it does happen. One of the important sources of gravitational waves for the proposed space based gravitational wave detector called LISA is a neutron star or black hole formed from the collapse of a star which orbits a supermassive black hole at the center of a galaxy. The detailed nature of the waves emitted depend upon the trajectory of the orbiting body. This in turn depends on the force that the emitted gravitational radiation emits on the orbiting body. Thus it is very important to compute this force. It will be possible to involve both undergraduate and graduate students in many of these projects. There is along history of undergraduate and graduate students working on these types of projects and gaining training in both numerical and analytical research techniques as well as being coauthors on publications.