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A Dynamical Systems Approach to Schwarzschild Null Geodesics · Around

2011

A Dynamical Systems Approach to Schwarzschild Null Geodesics

Belbruno, Edward, Pretorius, Frans

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The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective.

Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential.
We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions.
All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole.

Built on

A. S. Eddington, Nature 113
1924
Earlier work this paper cites.
D. Finkelstein, Phys. Rev. 110
1958
Earlier work this paper cites.
R.P.Kerr and A. Schild, IV Centenario Della Nascita di Galileo Galilei
1964
Earlier work this paper cites.
R. McGehee, Comment. Math. Helveti, 56
1981
Earlier work this paper cites.
R. Moeckel, Comm. Math. Phys., 150
1992
Earlier work this paper cites.
W. M. Vieira and P. S. Letelier, Phys. Rev. Lett. 76
1996
Earlier work this paper cites.

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Later among the works it cites.
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2009
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