Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-05-24
Class.Quant.Grav. 14 (1997) 489-498
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, a plain TeX file, submitted to ``Classical and Quantum Gravity''
Scientific paper
10.1088/0264-9381/14/2/021
In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is certainly correct, we show that the conclusions drawn from that fact were unwarranted, namely that this irregularity caused such solutions not to be able to truly describe pure gravitational waves. In this article, we resolve the paradox---since such first-order solutions must always have singular lines in space for all sufficiently large values of $r$---by showing that if we perturbatively iterate the solution up to the third order in small quantities, there are acceptable regular solutions. That these solutions become flat before they become non-twisting tells us something interesting concerning the general behavior of solutions describing gravitational radiation from a bounded source.
Finley Daniel J.
III
Plebański Jerzy F.
Przanowski Maciej
No associations
LandOfFree
An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox' does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox', we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox' will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-685375