“Symplectic Ray Tracing: Ray Tracing with Hamiltonian Dynamics in Black-Hole Spacetime”

  • ©Tetsu Satoh, Haruo Takemura, and Naokazu Yokoya



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    Symplectic Ray Tracing: Ray Tracing with Hamiltonian Dynamics in Black-Hole Spacetime

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    This technical sketch presents symplectic ray tracing, a novel approach to extend ray tracing in curved spacetime with black- holes. In conventional studies of visualizing black-hole spacetime, the path of light is computed by solving geodesic equations numerically. However, ray tracing based on the geodesic equation suffers from some problems concerning computational cost and accuracy of results. In order to overcome such problems, we have developed symplectic ray tracing based on Hamilton’s canonical equation instead of the geodesic equation. Hamilton’s canonical equation can be numerically solved by a symplectic process suited to long-time computation in black-hole spacetime.


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    3. Yoshida, H. (1993). Recent progress in the theory and application of symplectic integrators. Celestial Mechanics and Dynamical Astronomy, 56, 27-43.

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