In a stationary space‐time the brachistochrone problem can be formulated in two different ways, viz., to find the path of shortest travel time with prescribed specific energy from one space‐point to another (i) measured in terms of proper time or (ii) measured in terms of the time coordinate distinguished by the stationarity assumption. It is shown that in the static case both brachistochrone problems can be reduced to geodesic problems of appropriate Riemannian three‐metrics, in close analogy to the brachistochrone problem in a Newtonian potential. In the stationary but nonstatic case, however, this is true only for the proper time brachistochrones, whereas the coordinate time brachistochrones are influenced by a sort of Coriolis force. These results are illustrated by calculating the brachistochrones in Rindler, Schwarzschild, and Gödel space‐times.
Skip Nav Destination
Article navigation
November 1991
Research Article|
November 01 1991
The brachistochrone problem in a stationary space‐time
V. Perlick
V. Perlick
Institut für Theoretische Physik der TU Berlin, Sekr. PN 7‐1, Hardenbergstrasse 36, 1000 Berlin 12, Germany
Search for other works by this author on:
V. Perlick
Institut für Theoretische Physik der TU Berlin, Sekr. PN 7‐1, Hardenbergstrasse 36, 1000 Berlin 12, Germany
J. Math. Phys. 32, 3148–3157 (1991)
Article history
Received:
May 14 1991
Accepted:
July 02 1991
Citation
V. Perlick; The brachistochrone problem in a stationary space‐time. J. Math. Phys. 1 November 1991; 32 (11): 3148–3157. https://doi.org/10.1063/1.529472
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field
Marco Falconi, Nikolai Leopold
Quantum geodesics in quantum mechanics
Edwin Beggs, Shahn Majid
A sufficient criterion for divisibility of quantum channels
Frederik vom Ende
Related Content
Solving the brachistochrone and other variational problems with soap films
Am. J. Phys. (December 2010)
Restricted Brachistochrone
Phys. Teach. (September 2019)
Remarks on brachistochrone–tautochrone problems
Am. J. Phys. (March 1985)
The rolling unrestrained brachistochrone
Am. J. Phys. (September 1987)
Analytical synthesis of brachistochrones is an arbitrary velocity field
J. Acoust. Soc. Am. (August 2005)