SUMMARY
This discussion focuses on computing the spatial trajectories of massive test particles in Schwarzschild spacetime, specifically how to generate (r, φ) pairs for realistic plotting. The initial approach involved numerical integration of the equation of motion (dr/dφ)² = f(r), which presented challenges such as determining the sign of dr/dφ and handling numerical errors. Alternative methods discussed include using elliptic functions for exact solutions and applying the geodesic equation in (t, x, y) coordinates for better numerical stability. Participants shared insights on implementing these strategies using tools like Maxima and Stormer-Verlet integration.
PREREQUISITES
- Understanding of Schwarzschild geodesics
- Familiarity with numerical integration techniques
- Knowledge of elliptic functions and their implementations
- Experience with programming languages suitable for scientific computing, such as Python or Maxima
NEXT STEPS
- Research "Schwarzschild geodesics" for theoretical background
- Learn "numerical integration methods" such as Runge-Kutta or Stormer-Verlet
- Explore "elliptic functions" and their applications in physics
- Investigate programming techniques for plotting in Python or Maxima
USEFUL FOR
Physicists, computational scientists, and anyone interested in general relativity and the dynamics of particles in curved spacetime.