Motion of small bodies in general relativity: foundations and implementations of the self-force
arXiv:1006.3903
Abstract
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using perturbation theory. However, in order to relate the motion of the small body to the emitted waveform, one requires a model that is accurate on extremely long timescales. Additionally, in order to avoid intractable divergences, one requires a model that treats the small body as asymptotically small rather than exactly pointlike. Both of these difficulties can be resolved by using techniques of singular perturbation theory. I begin this dissertation with an analysis of singular perturbation theory on manifolds, including the common techniques of matched asymptotic expansions and two-timescale expansions. I then formulate a systematic asymptotic expansion in which the metric perturbation due to the body is expanded while a representative worldline is held fixed, and I contrast it with a regular expansion in which both the metric and the worldline must be expanded. This results in an approximation that is potentially uniformly accurate on long timescales. The equation of motion for the body's fixed worldline is determined by performing a local-in-space expansion in the neighbourhood of the body. Using this local expansion as boundary data, I construct a global solution to the perturbative Einstein equation. To concretely characterize orbits, I next devise a relativistic generalization of the Newtonian method of osculating orbits. Making use of this method and two-timescale expansions, I examine the utility of adiabatic approximations that can forgo an explicit calculation of the force.
246 pages, 15 figures, PhD thesis, abstract truncated to meet arXiv requirements
References in corpus (70)
- Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
- Relativistic tidal properties of neutron stars
- Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
- LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy
- An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
- Estimating spinning binary parameters and testing alternative theories of gravity with LISA
- Self-force via a Green's function decomposition
- Does backreaction enforce the averaged null energy condition in semiclassical gravity?
- Perturbative Approach to an orbital evolution around a Supermassive black hole
- Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
- The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission
- A Comparison of search templates for gravitational waves from binary inspiral
- Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism
- "Kludge" gravitational waveforms for a test-body orbiting a Kerr black hole
- Gravitational wave snapshots of generic extreme mass ratio inspirals
- Numerical Relativity and Compact Binaries
- Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations
- Celestial mechanics in Kerr spacetime
- Phasing of gravitational waves from inspiralling eccentric binaries
- Calculating the gravitational self force in Schwarzschild spacetime
- Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
- The use of Generalised Functions and Distributions in General Relativity
- A Rigorous Derivation of Electromagnetic Self-force
- Axiomatic approach to radiation reaction of scalar point particles in curved spacetime
- Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation
- Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
- The self-consistent gravitational self-force
- Gravitational self force and gauge transformations
- Multipolar equations of motion for extended test bodies in General Relativity
- Towards adiabatic waveforms for inspiral into Kerr black holes: II. Dynamical sources and generic orbits
- Nonrotating black hole in a post-Newtonian tidal environment
- Theorems on existence and global dynamics for the Einstein equations
- Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
- The adiabatic evolution of orbital parameters in the Kerr spacetime
- Low multipole contributions to the gravitational self-force
- Geometry and dynamics of a tidally deformed black hole
- Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation
- Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases
- Metric of a tidally distorted, nonrotating black hole
- Adiabatic radiation reaction to the orbits in Kerr Spacetime
- Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
- Limitations of the adiabatic approximation to the gravitational self-force
- Self-force on extreme mass ratio inspirals via curved spacetime effective field theory
- m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
- Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies
- Energy conservation for point particles undergoing radiation reaction
- An introduction to the Lorentz-Dirac equation
- Second-order gravitational self-force
- Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
- Covariant Self-force Regularization of a Particle Orbiting a Schwarzschild Black Hole - Mode Decomposition Regularization -
- Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space
- Strategies for observing extreme mass ratio inspirals
- Multi-scale analysis of the electromagnetic self-force in a weak gravitational field
- Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime
- Construction of the second-order gravitational perturbations produced by a compact object
- Singular perturbation techniques in the gravitational self-force problem
- Self-forces from generalized Killing fields
- Retarded coordinates based at a world line, and the motion of a small black hole in an external universe
- Self-forces on extended bodies in electrodynamics
- Photon rockets and gravitational radiation
- A light-cone gauge for black-hole perturbation theory
- Quasi-local contribution to the gravitational self-force
- Adiabatic Expansion for Metric Perturbation and the condition to solve the Gauge Problem for Gravitational Radiation Reaction Problem
- Two-timescale adiabatic expansion of a scalar field model
- Initial data for fluid bodies in general relativity
- Post-Newtonian expansions for perfect fluids
- Regular second order perturbations of binary black holes: The extreme mass ratio regime
- Equations of Motion in General Relativity of a Small Charged Black Hole
- Existence of families of spacetimes with a Newtonian limit
- The fast Newtonian limit for perfect fluids