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written by Wolfgang Christian
The Particle Worldline model computes and displays the trajectory of a test particle in the vicinity of a black hole using Schwarzschild coordinates.  It was created for the study of Einstein's theory of general relativity and the Schwarzschild metric.  

The model has input fields displaying the Schwarzschild coordinates and their rates of change as well as the energy E and and angular momentum L of the particle.  Conservation laws and the speed of light impose restrictions on the dynamical variables and these restrictions are enforced when entering values or dragging the particle.  For example, if a user changes the default value of dr/dt to 10, the model automatically reduces the value to 0.685 because the particle speed cannot exceed the speed of light c=1.

The Particle Worldline model a supplemental simulation for the article "When action is not least for orbits in general relativity" by C. G. Gray and Eric Poisson in the American Journal of Physics 79(1), 43-55 (2011) and has been approved by the authors and the American Journal of Physics (AJP) editor.  The simulation was developed using the Easy Java Simulations (EJS) modeling tool and is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_gr_ParticleWorldline.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.
View the source code document attached to this resource
  • Particle Worldline Source Code
    The source code zip archive contains an XML representation of the Particle Worldline model.   Unzip this archive in your EJS workspace to compile and run this model using EJS.
Subjects Levels Resource Types
- General Relativity
= Black Holes
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
- Learners
- Educators
- application/java
  • Currently 0.0/5

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Access Rights: Free access
License: This material is released under a GNU General Public License Version 3 license. Additional information is available.
Rights Holder: Wolfgang Christian
Keywords: General Relativity, Schwarzschild
Record Cloner: Metadata instance created October 30, 2010 by Wolfgang Christian
Record Updated: Jun 11, 2014 by Andreu Glasmann
Last Update
when Cataloged:
October 30, 2010
Other Collections:
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
W. Christian, Computer Program PARTICLE WORLDLINE MODEL, Version 1.0 (2010), WWW Document, (
W. Christian, Computer Program PARTICLE WORLDLINE MODEL, Version 1.0 (2010), <>.
APA Format
Christian, W. (2010). Particle Worldline Model (Version 1.0) [Computer software]. Retrieved March 29, 2015, from
Chicago Format
Christian, Wolfgang. "Particle Worldline Model." Version 1.0. (accessed 29 March 2015).
MLA Format
Christian, Wolfgang. Particle Worldline Model. Vers. 1.0. Computer software. 2010. Java 1.5. 29 Mar. 2015 <>.
BibTeX Export Format
@misc{ Author = "Wolfgang Christian", Title = {Particle Worldline Model}, Month = {October}, Year = {2010} }
Refer Export Format

%A Wolfgang Christian
%T Particle Worldline Model
%D October 30, 2010
%O 1.0
%O application/java

EndNote Export Format

%0 Computer Program
%A Christian, Wolfgang
%D October 30, 2010
%T Particle Worldline Model
%7 1.0
%8 October 30, 2010

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Citation Source Information

The AIP Style presented is based on information from the AIP Style Manual.

The APA Style presented is based on information from APA Electronic References.

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Particle Worldline Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Particle Worldline Model.

relation by Wolfgang Christian

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