This award supports a program of theoretical research on consequences of quantum field processes both at the late stage of the evolution of black holes and at the initial stage of the early universe. A framework called stochastic gravity is used to study these issues because it is especially well suited for treating quantum field fluctuations that have not been included in previous work on these topics. Quantitative results may be obtained from the Einstein-Langevin equation defining this framework. Techniques and concepts from quantum information theory are also used to address the black hole information issue. These methods may also be used to calculate the gravitational wave form and emitted energy from binary systems potentially detectable by LIGO and LISA.
Determination of the magnitude of metric fluctuations near the black hole horizon due to quantum fields is essential to finding a solution to the backreaction problem: how Hawking radiation affects the state and dynamics of a black hole, both under quasi-equilibrium (in a box) and non-equilibrium (evaporating) conditions. Stochastic gravity provides an easier to implement route towards structure formation from second order metric perturbations needed in inflationary cosmologies based on higher order curvature theories. A new formulation of gravitational wave dynamics for binary masses with radiation reaction is useful for treating the self force on the small mass and backreaction of it on the motion of the large mass self-consistently without making the slow motion or the weak field assumptions.
Fluctuations are now believed to play a subtle yet pivotal role in governing the growth of multifarious forms in the physical world, from the small to the large, the extreme of it being the generation of structures in the universe. Galaxy formation can be traced to the growth of quantum fluctuations during the inflationary stage of the early universe. The PI is the originator of an extended theory of general relativity called stochastic semiclassical gravity which takes into account not only the mean values but also the fluctuations in the matter quantum field and the induced metric fluctuations of spacetime. The key ingredient is the so-called noise kernel which is the vacuum expectation value of the stress energy bitensor of the matter quantum field which provides the fluctuations which together with the mean values (semiclassical) act as source in the Einstein-Langevin equation. Backreaction refers to the effects of the quantum matter fields on the spacetime dynamics. This effect is significant usually only in very strong or rapidly changing gravitational fields as existed in the early universe or in the late stages of black hole collapse. But it could alter the state and evolution of the early universe and the final fate of a black hole -- whether it continues to collapse to a singularity, evaporates completely or settles into a ramnent. In these extreme conditions fluctuations also could become large and thus backreaction studies need be carried out in tether with fluctuation phenomena. The stochastic gravity program encompasses both of these ingredients and provides the backreaction in a self-consistent manner. One of the three major components in this funded research aims at the calculation of the noise kernel to enable eventually the solution of the Einstein-Langevin equation for the fluctuations and backreaction effects. Such effects near the black hole horizon are viewed as crucial in determining whether the existing theoretical description of its eventual fate is sound. But there is no analytic solution and one needs to resort to approximations, which we sought. We also went an alternate way, making use of the known correspondence between the Schwarzschild spacetime (Hartle-Hawking state) for the black hole and the static de Sitter spacetime (Gibbons-Hawking state). We can calculate the exact form of the noise kernel in the de Sitter case and use the correspondence to obtain the behavior near the Schwarzschild horizon. The second major component is to make use of the quantum black hole atom analogy to try to understand how a black hole behaves in a quantum field such as how its own (Hawking) radiation may affect its energetics (level shifts) and dynamics (fate). We can borrow many physical insights gained in the oldest yet still vibrant field of atomic-optical physics. In fact studies by Bekenstein and others have suggested that a quantum black hole may have an evenly spaced energy spectrum. This was what prompted the PI to begin exploring (harmonic) atom-field interactions in the last decade, especially for the exploration of its radiation, backreaction, fluctuations and quantum information aspects. The special value we brought to this endeavor is the introduction of sophisticated quantum field theory techniques and nonequilibrium statistical mechanical ideas (known as nonequilibrium quantum field theory – read, e.g., Cambridge U monograph by Calzetta and Hu, 2008) . Nonequilibrium upgrade of black hole thermodynamics is needed to address the fluctuations and backreaction issues. The third major component of our research is quantum information in detector (black hole atom) – quantum field systems, with special attention paid to important issues in cosmological and black hole quantum processes. We focus on two key processes: quantum decoherence and entanglement. Decoherence studies how quantum phase information is habitually suppressed when the system is subjected to influences from its environments. This bears on the important issue of explaining why the fundamental laws are quantum and yet we see classical behavior around us. Schrodinger referred to quantum entanglement as the uniquely quantum feature and is the major resource of speedups in quantum computers. We focus on the analysis of quantum information in detector-field systems using quantum open system ideas and quantum field theoretical methods. These analyses can provide much needed solid quantitative understanding of some key issues in the development of a nascent field known as relativistic quantum information. They also paved the way for solid inquires into issues of fundamental interest in black hole physics such as the "information loss" puzzle and can provide a serious quantifiable base to those who wish to venture for Wheeler’s "it from bit" paradigm or Lloyd’s computing universe big ideas.
