http://arxiv.org/abs/1806.09022
Bound geodesic orbits of black holes are very well understood. Given a Kerr black hole of mass $M$ and spin $S = aM^2$, it is a simple matter to characterize its orbits as functions of the orbital geometry. How do the orbits change if the black hole is itself evolving? In this paper, we consider a process that changes a black hole’s mass and spin, acting such that the spacetime is described by the Kerr solution at any moment. Provided this change happens slowly, the orbit’s action variables $J_r$, $J_\theta$, and $J_\phi$ are {\it adiabatic invariants}, and thus are constant during this process. By enforcing adiabatic invariance of the actions, we deduce how an orbit evolves due to changes in the black hole’s mass and spin. We illustrate our results by examining the inspiral of a small body into a black hole and accounting for the change to the hole’s mass and spin due to the gravitational radiation absorbed by the event horizon. We find a correction to the gravitational-wave phase evolution which is so small that it is essentially negligible. This is consistent with previous literature that finds negligible impact due to black hole mass and spin evolution, although it corrects the previous method, and changes the (very small) magnitude of the effect. The impact of mass and spin evolution that we find should emerge from a self-consistent self-force analysis of a large mass-ratio binary, with the terms we find here appearing at second order in the self force’s effects.
S. Hughes
Tue, 26 Jun 18
50/71
Comments: 8 pages, 4 figures. Submitted to Phys Rev D
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