Dijs de Neeling
PO Box 72, 9700 AB Groningen, The Netherlands
Van Swinderen Institute for Particle Physics and Gravity, University of Groningen
Publications:
de Neeling D., Roest D., Seri M., Waalkens H.
Extremal Black Holes as Relativistic Systems with Kepler Dynamics
2024, vol. 29, no. 2, pp. 344-368
Abstract
The recent detection of gravitational waves emanating from inspiralling black hole
binaries has triggered a renewed interest in the dynamics of relativistic two-body systems. The
conservative part of the latter are given by Hamiltonian systems obtained from so-called post-
Newtonian expansions of the general relativistic description of black hole binaries. In this paper
we study the general question of whether there exist relativistic binaries that display Keplerlike
dynamics with elliptical orbits. We show that an orbital equivalence to the Kepler problem
indeed exists for relativistic systems with a Hamiltonian of a Kepler-like form. This form is
realised by extremal black holes with electric charge and scalar hair to at least first order in
the post-Newtonian expansion for arbitrary mass ratios and to all orders in the post-Newtonian
expansion in the test-mass limit of the binary. Moreover, to fifth post-Newtonian order, we
show that Hamiltonians of the Kepler-like form can be related explicitly through a canonical
transformation and time reparametrisation to the Kepler problem, and that all Hamiltonians
conserving a Laplace – Runge – Lenz-like vector are related in this way to Kepler.
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