Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation
Abstract
In this work, the authors study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. It is found, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. The authors present the solutions of this fourth order equation and find that they are able to recover all of the standard NewtonEuler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, the authors make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales for outside of fundamental sources, or on the very smallest ones within their interiors. This study enables the deduction that even though the familiar second order Poisson gravitational equationmore »
 Authors:

 Univ. of Connecticut, Storrs, CT (United States)
 NASA/Goddard Space Flight Center, Greenbelt, MD (United States)
 Publication Date:
 OSTI Identifier:
 7206888
 Resource Type:
 Journal Article
 Journal Name:
 General Relativity and Gravitation; (United States)
 Additional Journal Information:
 Journal Volume: 26:4; Journal ID: ISSN 00017701
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GRAVITATION; POISSON EQUATION; CLASSICAL MECHANICS; CONFORMAL INVARIANCE; GENERAL RELATIVITY THEORY; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; INVARIANCE PRINCIPLES; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; 661310*  Relativity & Gravitation (1992)
Citation Formats
Mannheim, P D, and Kazanas, D. Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation. United States: N. p., 1994.
Web. doi:10.1007/BF02105226.
Mannheim, P D, & Kazanas, D. Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation. United States. https://doi.org/10.1007/BF02105226
Mannheim, P D, and Kazanas, D. Fri .
"Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation". United States. https://doi.org/10.1007/BF02105226.
@article{osti_7206888,
title = {Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation},
author = {Mannheim, P D and Kazanas, D},
abstractNote = {In this work, the authors study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. It is found, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. The authors present the solutions of this fourth order equation and find that they are able to recover all of the standard NewtonEuler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, the authors make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales for outside of fundamental sources, or on the very smallest ones within their interiors. This study enables the deduction that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary. 17 refs., 1 fig.},
doi = {10.1007/BF02105226},
url = {https://www.osti.gov/biblio/7206888},
journal = {General Relativity and Gravitation; (United States)},
issn = {00017701},
number = ,
volume = 26:4,
place = {United States},
year = {1994},
month = {4}
}