Secondorder gravitational selfforce
Abstract
We derive an expression for the secondorder gravitational selfforce that acts on a selfgravitating compact object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the firstorder gravitational selfforce. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the secondorder gravitational selfforce. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveform templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational selfforce will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational waves that are emitted from extreme massratio binaries.
 Authors:
 Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)
 Publication Date:
 OSTI Identifier:
 20871410
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 74; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.74.084018; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; DATA ANALYSIS; EMISSION; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; MASS; SPACETIME; WAVE FORMS
Citation Formats
Rosenthal, Eran. Secondorder gravitational selfforce. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.74.084018.
Rosenthal, Eran. Secondorder gravitational selfforce. United States. doi:10.1103/PHYSREVD.74.084018.
Rosenthal, Eran. 2006.
"Secondorder gravitational selfforce". United States.
doi:10.1103/PHYSREVD.74.084018.
@article{osti_20871410,
title = {Secondorder gravitational selfforce},
author = {Rosenthal, Eran},
abstractNote = {We derive an expression for the secondorder gravitational selfforce that acts on a selfgravitating compact object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the firstorder gravitational selfforce. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the secondorder gravitational selfforce. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveform templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational selfforce will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational waves that are emitted from extreme massratio binaries.},
doi = {10.1103/PHYSREVD.74.084018},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 74,
place = {United States},
year = 2006,
month =
}

Investigating the evolution of disk galaxies and the dynamics of protostellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using twodimensional Cartesian or polar coordinates. In Cartesian coordinates, the calculations of the hydrodynamics and selfgravitational forces are relatively straightforward for attaining secondorder accuracy. However, in polar coordinates, a secondorder calculation of selfgravitational forces is required for matching the secondorder accuracy of hydrodynamical schemes. We present a direct algorithm for calculating selfgravitational forces with secondorder accuracy without artificial boundary conditions. The Poisson integral in polar coordinates ismore »

Highorder postNewtonian fit of the gravitational selfforce for circular orbits in the Schwarzschild geometry
We continue a previous work on the comparison between the postNewtonian (PN) approximation and the gravitational selfforce (SF) analysis of circular orbits in a Schwarzschild background. We show that the numerical SF data contain physical information corresponding to extremely high PN approximations. We find that knowing analytically determined appropriate PN parameters helps tremendously in allowing the numerical data to be used to obtain higher order PN coefficients. Using standard PN theory we compute analytically the leading 4PN and the nexttoleading 5PN logarithmic terms in the conservative part of the dynamics of a compact binary system. The numerical perturbative SF resultsmore » 
Selfconsistent gravitational selfforce
I review the problem of motion for small bodies in general relativity, with an emphasis on developing a selfconsistent treatment of the gravitational selfforce. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed. I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving selfconsistent equationsmore » 
Analytic prediction of the exact thermodynamics of a firstorder structural phase transition: A practical secondorder selfconsistent phonon theory
We examine an extension of selfconsistent phonon theory (SCPT) that allows for the explicit evaluation of secondorder corrections to the free energy for both the high and lowtemperature phases for a system undergoing a firstorder structural phase transition. The motivation for the inclusion of these terms stemmed from the manybody theory developed to treat the lattice vibrations in anharmonic crystals. This approach does not modify predictions for the phonon frequencies that would be observed by inelastic neutron scattering; however, we show that these higherorder contributions to the free energy are [ital essential] if the bulk limit of the equilibrium thermodynamicmore »