Kastor-Traschen Black Holes, Null Geodesics and Conformal Circles

Details Kastor-Traschen Black Holes, Null Geodesics and Conformal Circles Kastor-Traschen Black Holes, Null Geodesics and Conformal Circles

2011-10-10

arxiv.org/abs/1110.2091v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 24 figures

Scientific paper

The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the projection to the space of orbits of the timelike conformal retraction. It is found that these projected light rays arise as integral curves of a system of third order ODEs. In the one-centre case, we discuss this system and demonstrate a link to conformal circles in the limit as the cosmological constant tends to zero. We also show how to construct analytic expressions for the projected null geodesics by exploiting a well-known diffeomorphism between the K-T metric and extremal Reissner-Nordstrom deSitter. We make some remarks about the two-centre case and demonstrate that a special subset of the projected null geodesics here arises as a set of integral curves of the third-order system in the one-centre case.

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