Chad R. Galley

Classical Mechanics of Nonconservative Systems

Hamiltons principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamiltons principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamiltons principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics. Thus, dissipative effects, for example, can be studied with new tools that may have applications in a variety of disciplines. The new formalism is demonstrated by two examples of nonconservative systems: an object moving in a fluid with viscous drag forces and a harmonic oscillator coupled to a dissipative environment.

Radiation reaction and gravitational waves in the effective field theory approach

We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including radiation reaction forces and gravitational wave emission) and hereditary terms in the post-Newtonian approximation (including memory, tail and other causal, history-dependent integrals) within the EFT approach. We also provide a consistent formulation of the radiation sector in the equivalent effective field theory approach of Kol and Smolkin.

Self-force on extreme mass ratio inspirals via curved spacetime effective field theory

In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of the self-force on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, which in this problem are the size of the compact object

Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space

{r}_{m}

Fast prediction and evaluation of gravitational waveforms using surrogate models

and the radius of curvature of the background spacetime

Reduced Basis Catalogs for Gravitational Wave Templates

\mathcal{R}

Radiation reaction at 3.5 post-Newtonian order in effective field theory

such that

Finite Size Corrections to the Radiation Reaction Force in Classical Electrodynamics

\ensuremath{\epsilon}\ensuremath{\equiv}{r}_{m}/\mathcal{R}\ensuremath{\ll}1

Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models

, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. The equation of motion of an effective relativistic point particle coupled to the gravitational waves generated by its motion in a curved background spacetime can be derived without making a slow motion or weak field approximation, as was assumed in earlier EFT treatment of post-Newtonian binaries. Ultraviolet divergences are regularized using Hadamards partie finie to isolate the nonlocal finite part from the quasilocal divergent part. The latter is constructed from a momentum space representation for the graviton retarded propagator and is evaluated using dimensional regularization in which only logarithmic divergences are relevant for renormalizing the parameters of the theory. As a first important application of this framework we explicitly derive the first-order self-force given by Mino, Sasaki, Tanaka, Quinn, and Wald. Going beyond the point particle approximation, to account for the finite size of the object, we demonstrate that for extreme mass ratio inspirals the motion of a compact object is affected by tidally induced moments at

Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

O({\ensuremath{\epsilon}}^{4})