Book A Study of Black Hole Formation and Evaporation Via the D1D5 CFT Dual PDF Free

A Study of Black Hole Formation and Evaporation Via the D1D5 CFT Dual PDF
By:Zachary Lee Carson
Published on 2016 by

Several advancements in our understanding of fuzzball black have been made via the study of a dual Conformal Field Theory. In this approach, the full picture of black hole formation and eventual evaporation is expected to correspond to thermalization in the CFT dual. In other words, an initial set of high-energy wavepackets that 'break up' into a large quantity of low-energy excitations in the CFT should be the dual to an initial set of high-energy infalling particles forming a black hole that then evaporates via a large quantity of low-energy Hawking radiation in the gravity description. The nature of a fuzzball's CFT dual depends on particular parameters of the underlying gravity theory, its moduli space, and it is conjectured that some choice of parameters is dual to a particularly simple `orbifold' CFT. Calculations at this orbifold point match some semi-classical results, but it is also clear that the orbifold point is does not exactly match the behavior of gravity as we know it. It is thus necessary to move away from this orbifild point via the perturbative application of a deformation operator. A framework for studying deformations away from the orbifold point was developed some time ago, but its application was previously limited to the simplest of tree-level processes. My work extends this framework to all tree-level processes. At this stage, there is no clear indication of thermalization. In addition, analysis is muddied by a change in the Hilbert space of the CFT. This makes comparisons between initial and final states difficult to perform. To address this, the framework was further extended to include a simple one-loop process. This process maintains a consistent Hilbert space between in and out states, allowing a more straightforward search for thermalization effects. Furthermore, certain patterns occurred when comparing the one-loop results to the tree-level process that constitutes the loop's first half. It is thus natural to conjecture that some of these patterns may remain at even higher orders. In addition to this work, I also present detailed analysis of a simplifying regime known as the 'continuum limit.' In this limit, the energy of the system is taken to be much larger than the size of the individual quanta, so that excitation levels appear continuous rather than discrete. This is exactly the regime of black hole formation. It also greatly simplifies the results of our calculations, which is of particular importance when dealing with the otherwise intractable expressions found in even the simplest one-loop case. While my work has not by any means succeeded in completing the ideal picture of black hole formation and subsequent evaporation, it provides a solid foundation upon which one may continue the search. By maintaining a consistent Hilbert space, the new one-loop result is readily extendable via a method of repeated application, which is not the case for the tree-level calculations. For the same reason it provides a more accessible place to search for wave packet splitting. And while the analytic results are particularly messy, they are accessible enough to facilitate future numerical work. Furthermore, a large number of useful relations have been proven to all orders of the twist portion of the deformation.

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