Radiation reaction and self-force in curved spacetime in a field theory approach
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This dissertation, in three parts, presents self-consistent descriptions for the motion of relativistic particles and compact objects in an arbitrary curved spacetime from a field theory approach and depicts the quantum and stochastic (part I), semiclassical (parts I and II), and completely classical regimes (part III).
In the semiclassical limit of an open quantum system description, the particle acquires a stochastic component in its dynamics. The interrelated roles of noise, decoherence, fluctuations and dissipation are prominently manifested from a stochastic field theory viewpoint and highlighted with our derivations of Langevin equations for the particle in curved space, which are useful for studying influences imparted by a stochastic source. We also derive non-local and history-dependent equations for radiation reaction and self-force in a curved spacetime when the stochastic sources are negligible.
When the scales of the mass and the field are very different, as for an astrophysical mass or compact object, the stochastic features of the system are strongly suppressed and the stochastic description yields a (semiclassical) effective field theory. The appropriate expansion parameter $\mu$ is the ratio formed by the size of the compact object and the background curvature scale. Within an effective field theory framework we derive the second order self-force and the leading order contributions to the equations of motion from spin-orbit and spin-spin interactions on a compact object. The finite size of the compact body affects its motion at $O(\mu^4)$ and the self-force at $O(\mu^5)$. These results are useful for constructing more accurate templates that the space-based interferometer LISA will need for parameter estimation.
Within a purely classical setting we introduce a new framework that describes fully relativistic gravitating binary systems, possibly with comparable masses, and allows for the background geometry to dynamically respond with the motions and influences of the compact objects and gravitational waves. The approach self-consistently incorporates mutual action and backreaction on every component in the total system. We derive the equations of motion and identify the parameter regimes where this new approach is applicable with the aim of establishing a common framework applicable to the detection ranges of both LIGO and LISA interferometers.