Next Article in Journal
New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs
Next Article in Special Issue
relxill_nk: A Relativistic Reflection Model for Testing Einstein’s Gravity
Previous Article in Journal
Towards a Unified Quark-Hadron-Matter Equation of State for Applications in Astrophysics and Heavy-Ion Collisions
Article Menu
Issue 6 (June) cover image

Export Article

Open AccessArticle
Universe 2018, 4(6), 68; https://doi.org/10.3390/universe4060068

Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration

1
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
2
Faculty of Science, Chandrakasem Rajabhat University, Bangkok 10900, Thailand
3
School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
*
Author to whom correspondence should be addressed.
Received: 1 April 2018 / Revised: 23 May 2018 / Accepted: 24 May 2018 / Published: 28 May 2018
(This article belongs to the Special Issue Gravity, Black Holes and Cosmology XXI)
  |  
PDF [516 KB, uploaded 28 May 2018]
  |  

Abstract

Geodesics (by definition) have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i / d t 2 can very easily be non-zero, and the coordinate velocity d x i / d t can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit—for both astrophysical and idealised black holes—where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i / d t 2 is best interpreted in terms of horizon-penetrating coordinates. View Full-Text
Keywords: geodesic equation; coordinate velocity; coordinate acceleration; horizon-penetrating coordinates; horizon-non-penetrating coordinates geodesic equation; coordinate velocity; coordinate acceleration; horizon-penetrating coordinates; horizon-non-penetrating coordinates
Figures

Graphical abstract

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Boonserm, P.; Ngampitipan, T.; Visser, M. Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration. Universe 2018, 4, 68.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Universe EISSN 2218-1997 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top