skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The Newtonian limit at intermediate energies

Abstract

We study the metric solutions for the gravitational equations in Modified Gravity Models (MGMs). In models with negative powers of the scalar curvature, we show that the Newtonian Limit (NL) is well defined as a limit at intermediate energies, in contrast with the usual low energy interpretation. Indeed, we show that the gravitational interaction is modified at low densities or low curvatures.

Authors:
 [1]
  1. Department of Physics and Astronomy, University of California, Irvine, California 92697 (United States)
Publication Date:
OSTI Identifier:
20782663
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.064029; (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; DENSITY; FIELD EQUATIONS; GRAVITATION; GRAVITATIONAL INTERACTIONS; MATHEMATICAL SOLUTIONS; SCALARS

Citation Formats

Cembranos, J.A.R. The Newtonian limit at intermediate energies. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.73.064029.
Cembranos, J.A.R. The Newtonian limit at intermediate energies. United States. doi:10.1103/PHYSREVD.73.064029.
Cembranos, J.A.R. Wed . "The Newtonian limit at intermediate energies". United States. doi:10.1103/PHYSREVD.73.064029.
@article{osti_20782663,
title = {The Newtonian limit at intermediate energies},
author = {Cembranos, J.A.R.},
abstractNote = {We study the metric solutions for the gravitational equations in Modified Gravity Models (MGMs). In models with negative powers of the scalar curvature, we show that the Newtonian Limit (NL) is well defined as a limit at intermediate energies, in contrast with the usual low energy interpretation. Indeed, we show that the gravitational interaction is modified at low densities or low curvatures.},
doi = {10.1103/PHYSREVD.73.064029},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • The natural generalization of the snowplow equation in two-dimensional axisymmetric or Cartesian geometries is a Newtonian approximation in which the possibility of surface deformation is admitted. Such a general Newtonian approximation is derived from the Lagrangian fluid equations, using a ideal-gas model in the limit of strong shock and high density ratio across the shock front. In one dimension the result reduces properly to the snowplow equation. In two dimensions, if the surface is constrained and the motion steady, the result consists of the Newtonian plus Busemann'' terms. The general result contains in addition a Coriolis term. The general theorymore » is applied to the evaluation of the pressure on the surface of a conical plasma whose vertex angle is decreasing uniformly with time. Although the results are derived for an ideal-gas model, they are applicable whenever dissociation and ionization take place behind a strong shock front. (auth)« less
  • The canonical formalism is applied to self-gravitating perfect fluids with particular emphasis on recovering the correct nonrelativistic limit also in (quasi-) Hamiltonian form. We use essentially Lagrangian coordinates by considering the fluid defined by a map from space-time into a three-dimensional material manifold which is equipped with a volume element representing physically the matter (baryon number) density. By eliminating the coordinate freedom in this material space the usual matter conservation and (relativistic) Euler equations are recovered in a (3+1)-dimensional formalism which makes it very easy to compare them to their nonrelativistic limits. By splitting the 3-metric and its canonical momentamore » into a conformal part and the determinant we arrive at a system of evolution and constraint equations for the gravitational field that also has a well-defined Newtonian limit provided the geometric version of the Newtonian theory is also cast into an analogous (3+1)-dimensional form. Some of the evolution equations of the relativistic theory, however, become additional constraints in the limit which represents the freezing of the gravitational (or radiation) degrees of freedom. We then use this formalism to rederive the first-order post-Newtonian approximation and obtain the standard results in a flexible geometrical form since no gauge or coordinate conditions need be imposed in advance.« less
  • The asymptotic approximation scheme based on the theory of the Newtonian limit developed in the preceding paper is applied to the gravitational radiation-reaction problem. All divergences encountered in previous approaches disappear: For any epsilon the asymptotic approximation is finite to all orders we have calculated, even beyond radiation-reaction order. This is because the divergent terms in previous work were misordered, and make finite contributions to coefficients of lower-order terms in the asymptotic expansion. The logarithmic divergences, in particular, turn up as an epsilon/sup 10/ lnepsilon term in the asymptotic expansion (i.e., between 2.5 and 3 post-Newtonian order) which shows thatmore » the relativistic sequence is not C/sup infinity/ at epsilon = 0. This does not, however, affect the asymptotic convergence of the approximation. The radiation-reaction terms are used to calculate the period shortening of a nearly-Newtonian binary system directly from the equations of motion, avoiding the well-known difficulties associated with energy in general relativity. It is proved that the prediction derived from the standard quadrupole formula applies in the Newtonian limit. It is also shown that random data for the initial gravitational wave field do not affect the calculation of radiation reaction, even if their amplitude is of first post-Newtonian order.« less
  • We examine the gravitational radiation emitted by a sequence of spacetimes whose near-zone Newtonian limit we have previously studied. The spacetimes are defined by initial data which scale in a Newtonian fashion: the density as epsilon/sup 2/, velocity as epsilon, pressure as epsilon/sup 4/, where epsilon is the sequence parameter. We asymptotically approximate the metric at an event which, as epsilon..-->..0, remains a fixed number of gravitational wavelengths distant from the system and a fixed number of wave periods to the future of the initial hypersurface. We show that the radiation behaves like that of linearized theory in a Minkowskimore » spacetime, since the mass of the metric vanishes as epsilon..-->..0. We call this Minkowskian far-zone limiting manifold FM; it is a boundary of the sequence of spacetimes, in which the radiation carries an energy flux given asymptotically by the usual far-zone quadrupole formula (the Landau-Lifshitz formula), as measured both by the Isaacson average stress-energy tensor in FM or by the Bondi flux on I/sup +//sub F//sub M/. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between I/sup +//sub epsilon/, the sequence of null infinities of the individual manifolds, and I/sup +//sub F//sub M/; and we examine the gauge-invariance of FM under certain gauge transformations. We also discuss the relation of this calculation with similar ones in the frame-work of matched asymptotic expansions and others based on the characteristic initial-value problem.« less