comparison of newtonian and special-relativistic trajectories with the general-relativistic trajectory for a low-speed weak-gravity system牛顿的比较和special-relativistic轨迹与广义相对论的低速低重力系统的轨迹.pdfVIP

Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak-Gravity System Shiuan-Ni Liang, Boon Leong Lan* School of Science, Monash University, Bandar Sunway, Selangor, Malaysia Abstract We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak- gravity system is not always well-approximated by the trajectories predicted by special-relativistic and Newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system). Citation: Liang S-N, Lan BL (2012) Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak- Gravity System. PLoS ONE 7(4): e34720. doi:10.1371/journal.pone.0034720 Editor: Gerardo Adesso, University of Nottingham, United Kingdom Received September 1, 2011; Accepted March 8, 2012; Published April 19, 2012 Copyright: 2012 Liang, Lan. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was funded by a Fundamental Research Grant S