Visualizing spacetime curvature via gradient flows. II. An example of the construction of a Newtonian analogue

Majd Abdelqader and Kayll Lake
Phys. Rev. D 86, 124037 – Published 19 December 2012

Abstract

This is the first in a series of papers in which the gradient flows of fundamental curvature invariants are used to formulate a visualization of curvature. We start with the construction of strict Newtonian analogues (not limits) of solutions to Einstein’s equations based on the topology of the associated gradient flows. We do not start with any easy case. Rather, we start with the Curzon-Chazy solution, which, as history shows, is one of the most difficult exact solutions to Einstein’s equations to interpret physically. A substantial part of our analysis is that of the Curzon-Chazy solution itself. Eventually we show that the entire field of the Curzon-Chazy solution, up to a region very “close” to the intrinsic singularity, strictly represents that of a Newtonian ring, as has long been suspected. In this regard, we consider our approach very successful. As regards the local structure of the singularity of the Curzon-Chazy solution within a fully general relativistic analysis, however, whereas we make some advances, the full structure of this singularity remains incompletely resolved.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 1 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.124037

© 2012 American Physical Society

Authors & Affiliations

Majd Abdelqader* and Kayll Lake

  • Department of Physics, Queen’s University, Kingston, Ontario, Canada K7L 3N6

  • *majd@astro.queensu.ca
  • lake@astro.queensu.ca

See Also

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 86, Iss. 12 — 15 December 2012

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×