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The Schwarzschild Problem in Astrophysics

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Abstract

The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field. Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold λ (a torus)pasted on the phase space. The flow on λ is fullycharacterized. Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B. Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel.

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Authors and Affiliations

  1. Gravitational Research Laboratory, Institute for Gravitation and Space Sciences, Str. Mendeleev 21-25, 70168, Bucharest, Romania

    Cristina Stoica

  2. Astronomical Observatory Cluj-Napoca, Astronomical Institute of the Romanian Academy, Str. Ciresilor 19, 3400, Cluj-Napoca, Romania

    Vasile Mioc

Authors
  1. Cristina Stoica
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  2. Vasile Mioc
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Stoica, C., Mioc, V. The Schwarzschild Problem in Astrophysics. Astrophysics and Space Science 249, 161–173 (1997). https://doi.org/10.1023/A:1000347014891

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  • DOI: https://doi.org/10.1023/A:1000347014891

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