2020/11/30 by Yen-Kheng Lim
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Constant (computer programming) #Constant curvature #Cosmology and Gravitation Theories #Curvature #Geodesic #Geometry #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Motion (physics) #Physics #Separable space #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.103.024007
published as Phys. Rev. D 103, 024007 (2021) · 27 pages, 9 figures. Typos corrected and references added
openalex created_date 2020/11/23 · openalex publication_date 2021/01/05 · arxiv created 2021/01/06 · arxiv updated 2021/01/07 · openalex updated_date 2026/08/05
In this paper we study the motion of photons or massless particles in the C metric with cosmological constant. The Hamilton-Jacobi equations are known to be completely separable, giving a Carter-like quantity Q which is a constant of motion. All possible trajectories are classified according to a two-dimensional parameter space representing the particle's angular momentum and energy scaled in units of Q. Exact solutions are given in the C metric coordinates in terms of Jacobi elliptic functions. Using the exact solutions, we find examples of periodic orbits on the photon surface.