Radiation reaction techniques in general relativity
Moxon, Jordan Emrys
This dissertation presents several results which pertain to self-interaction effects in general relativity. I first present a detailed review of the physics of gravitational radiation, and compact binaries in general, which provide the key motivation for detailed exploration of the physical processes and modelling of radiation reaction effects. In particular, extreme mass ratio inspirals (EMRIs) and intermediate mass ratio inspirals (IMRIs) are a promising source for current and near-future gravitational wave detectors, and detailed modeling of the resulting waveforms requires a deep understanding of the physics of self interactions. The first project which I present in this dissertation is the first derivation of the second-order self force for scalar and electromagnetic fields in flat spacetime. In the process of developing this derivation, several important mathematical subtleties in the definitions of bulk body parameters emerged, which become important at the same order at which gravitational self force computations are considered. Additionally, this self force is of intrinsic interest for charges accelerated by high-powered lasers and in astrophysical systems. Our derivation lays the ground work for future derivations of high order self force in curved spacetime, which may be important for testing alternative theories of gravity. The second project, which comprises the majority of this dissertation, details the development of a tapestry of approximations for highly accurate simulation of high mass ratio inspirals. Due to the precision requirements for waveform templates important for LISA data analysis, one of the significant goals of self force calculations is to compute waveforms that track the phase of the long evolution of EMRIs to a precision far better than one radian. One of the methods is a multiscale expansion which exploits the separation of scales between the slow radiation-reaction time and the fast orbital time. This dissertation discusses in detail the mathematical techniques of the multiscale approximation method and other approximations in the various regions of the spacetime. The techniques, which I develop in collaboration with Éanna Flanagan, Tanja Hin-derer, and Adam Pound, comprise the only currently available method of assuring sub-radianaccuracy in the computed waveform. The last project presented in this dissertation develops new techniques for quantizing theories which exhibit gauge degrees of freedom. We suggest a modification of the well-known Dirac bracket formalism. The alternative formalism may be more useful than the more frequently used methods of BRST quantization for derivations of local effects of dressed states. In addition, the modified Dirac bracket may be more computationally simple than the original, which may be of use for computations in intricate theories.
Mathematics; Physics; binary black holes; dirac brackets; gravitational waves; perturbation theory; self force; General Relativity; Astrophysics
Flanagan, Eanna E.
Niemack, Michael D.; Hartman, Thomas
Ph. D., Physics
Doctor of Philosophy
Attribution-ShareAlike 4.0 International
dissertation or thesis
Except where otherwise noted, this item's license is described as Attribution-ShareAlike 4.0 International