DOI: https://doi.org/10.30970/jps.15.3002
BRACHISTOCHRONE PROBLEM IN THE SCHWARZSCHILD METRIC
A. R. Kuzmak
Department for Theoretical Physics, Ivan Franko National University of Lviv,
12, Drahomanov St., Lviv, UA--79005, Ukraine
|
Journal of Physical Studies 15(3), Article 3002 [9 pages] (2011)
DOI: https://doi.org/10.30970/jps.15.3002 BRACHISTOCHRONE PROBLEM IN THE SCHWARZSCHILD METRICA. R. Kuzmak
Department for Theoretical Physics, Ivan Franko National University of Lviv, |
|
The brachistochrone problem in a weakly nonuniform gravitational field was obtained for the first time by Singh and Kumar in 1988. This equation has been obtained using the Newtonian mechanics. We have solved the brachistochrone problem in the Schwarzschild metric using the laws of general relativity. In this work we have obtained the brachistochrone equation and the equation for time. Also, we have obtained the relativistic equation for the uniform gravitational field. These results we have compared with the classical results.
PACS number(s): 04.20.Fy, 04.70.Bw, 95.30.Sf