Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole

Hans-Jürgen Schmidt
Phys. Rev. D 83, 124010 – Published 2 June 2011

Abstract

We deduce a new formula for the perihelion advance Θ of a test particle in the Schwarzschild black hole by applying a newly developed nonlinear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. The resulting formula has the structure Θ=c1c2ln(c32e2) with positive constants c1,2,3 depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities e<c3<1 showing that Θ as ec3.

  • Received 17 April 2011

DOI:https://doi.org/10.1103/PhysRevD.83.124010

© 2011 American Physical Society

Authors & Affiliations

Hans-Jürgen Schmidt*

  • Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany

  • *hjschmi@rz.uni-potsdam.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 83, Iss. 12 — 15 June 2011

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
×