Studies of Classical and Quantum Effects in Gravity

该奖项支持几个项目，这些项目涉及研究与宇宙学和黑洞有关的量子效应。同样的技术将被用来计算粒子在绕黑洞轨道运行时因发出引力辐射而感受到的力。当今宇宙学中最重要的观点之一是，宇宙在其历史早期经历了一个极快的膨胀过程，称为暴胀。在通货膨胀期间和之后不久，量子效应都非常重要。它们几乎总是使用一种被称为半经典近似的量子场论近似来计算。这一近似的有效性将被调查，因为它与膨胀周期和紧接在该周期之后发生的粒子产生有关。此外，还将研究量子场对黑洞事件视界的影响。视界是空间中光线可以离开黑洞的地方和不能离开的地方之间的边界。还将研究量子场对远离黑洞视界的几何体的影响与对远离静止恒星表面的几何体的影响之间的差异。当粒子绕黑洞轨道运行时，就会发出引力辐射，其影响可能会改变随后的轨道。如果粒子带电，也会发射电磁辐射。可以使用一种更简单的称为标量辐射的辐射来模拟这些辐射。将开展的项目包括计算这种标量辐射对绕黑洞轨道运行的粒子施加的力。一些最重要的膨胀预测，包括最终演化成星系的密度波动，依赖于量子效应，这些量子效应是使用半经典近似计算的。因此，确定这些近似是否在通货膨胀期间和通货膨胀后立即有效是极其重要的。如果在一些混乱的通胀情景下重新升温的计算无效，那么将有必要进行更困难的计算。在黑洞的情况下，有迹象表明，在某些特殊情况下，量子效应可能会对黑洞的事件视界产生如此重大的影响，以至于它们阻止了这种类型的黑洞的存在。目前还不清楚这种情况发生的可能性有多大，但重要的是调查它是否真的发生了。拟议中的空间引力波探测器LISA的重要引力波来源之一是中子星或黑洞，它是围绕星系中心的超大质量黑洞运行的恒星坍塌形成的。所发射的波的详细性质取决于轨道天体的轨迹。这又取决于所发射的引力辐射对轨道天体的作用力。因此，计算这个力是非常重要的。在许多这样的项目中，本科生和研究生都有可能参与。本科生和研究生从事这类项目的历史由来已久，他们接受了数值和分析研究技术方面的培训，也是出版物的合著者。

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.