Quick Search:

uzh logo
Browse by:
bullet
bullet
bullet
bullet

Zurich Open Repository and Archive

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-41724

D'Orazio, D J; Saha, P (2010). An analytic solution for weak-field Schwarzschild geodesics. Monthly Notices of the Royal Astronomical Society, 406(4):2787-2792.

[img]
Preview
Accepted Version
PDF (Accepted manuscript, Version 3)
166kB

View at publisher
[img]
Preview
Accepted Version
PDF (Accepted manuscript, Version 2)
165kB
[img]
Preview
Accepted Version
PDF (Accepted manuscript, Version 1)
165kB

Abstract

It is well known that the classical gravitational two-body problem can be transformed into a spherical harmonic oscillator by regularization. We find that a modification of the regularization transformation has a similar result to leading order in general relativity. In the resulting harmonic oscillator, the leading-order relativistic perturbation is formally a negative centrifugal force. The net centrifugal force changes sign at 3 Schwarzschild radii, which interestingly mimics the innermost stable circular orbit of the full Schwarzschild problem. Transforming the harmonic-oscillator solution back to spatial coordinates yields, for both time-like and null weak-field Schwarzschild geodesics, a solution for t, r, ϕ in terms of elementary functions of a variable that can be interpreted as a generalized eccentric anomaly. The textbook expressions for relativistic precession and light deflection are easily recovered. We suggest how this solution could be combined with additional perturbations into numerical methods suitable for applications such as relativistic accretion or dynamics of the Galactic Centre stars.

Citations

1 citation in Web of Science®
1 citation in Scopus®
Google Scholar™

Altmetrics

Downloads

50 downloads since deposited on 02 Mar 2011
11 downloads since 12 months

Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute for Computational Science
DDC:530 Physics
Language:English
Date:August 2010
Deposited On:02 Mar 2011 14:32
Last Modified:15 Jun 2014 17:35
Publisher:Wiley-Blackwell
ISSN:0035-8711
Additional Information:The definitive version is available at www.blackwell-synergy.com
Publisher DOI:10.1111/j.1365-2966.2010.16879.x
Related URLs:http://arxiv.org/abs/1003.5659

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page