We use computer algebra to derive the equations of motion from the Lagrangian, solve the equations of motion numerically, and plot the numerical solutions, to discover the difference between trajectories of a particle under gravity based on Newtonian theory and general relativity with the Schwarzschild and the Kerr metric.
REFERENCES
1.
G. C.
McGuire
, “Using computer algebra to investigate the motion of an electric charge in magnetic and electric dipole fields
,” Am. J. Phys.
71
, 809
–812
(2003
).2.
E. F. Taylor and J. A. Wheeler, Exploring Blacks: Introduction to General Relativity (Addison Wesley Longman, San Francisco, 2000).
3.
B. F. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1985).
4.
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
5.
The site 〈http://math.ucr.edu/home/baez/RelWWW/visual.html〉 collects computer simulations illustrating various aspects of relativity.
6.
The worksheet is available at 〈http://www.mapleapps.com/categories/science/physics/html/wangorbits.html〉.
7.
E. F.
Taylor
described such a condition as the “Principle of extremal aging” in his speech “The boundaries of nature: Special and general relativity and quantum mechanics, a second course in physics
,” Am. J. Phys.
67
, 369
–376
(1998
).8.
Reference 4, pp. 660–662.
9.
S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (Wiley, New York, 1983), p. 360.
10.
Reference 3, p. 298.
11.
D.
Wilkins
, “Bound geodesics in the Kerr metric
,” Phys. Rev. D
5
, 814
–822
(1972
).12.
M.
Johnston
and R.
Ruffini
, “Generalized Wilkins effect and selected orbits in a Kerr-Newman geometry
,” Phys. Rev. D
10
, 2324
–2329
(1974
).13.
Reference 4, p. 130.
14.
Reference 4, pp. 613–615.
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© 2004 American Association of Physics Teachers.
2004
American Association of Physics Teachers
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