Carter-like constants of motion in the Newtonian and relativistic two-center problems

Details Carter-like constants of motion in the Newtonian and relativistic two-center problems Carter-like constants of motion in the Newtonian and relativistic two-center problems

2010-09-15

arxiv.org/abs/1009.2839v2

Class.Quant.Grav.27:235021,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages; version to be published by Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/27/23/235021

In Newtonian gravity, a stationary axisymmetric system admits a third, Carter-like constant of motion if its mass multipole moments are related to each other in exactly the same manner as for the Kerr black-hole spacetime. The Newtonian source with this property consists of two point masses at rest a fixed distance apart. The integrability of motion about this source was first studied in the 1760s by Euler. We show that the general relativistic analogue of the Euler problem, the Bach-Weyl solution, does not admit a Carter-like constant of motion, first, by showing that it does not possess a non-trivial Killing tensor, and secondly, by showing that the existence of a Carter-like constant for the two-center problem fails at the first post-Newtonian order.

Affiliated with

Also associated with

No associations

Rating

Carter-like constants of motion in the Newtonian and relativistic two-center problems 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 Carter-like constants of motion in the Newtonian and relativistic two-center problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Carter-like constants of motion in the Newtonian and relativistic two-center problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-76882