Bound orbits of a slowly evolving black hole. (arXiv:1806.09022v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Hughes_S/0/1/0/all/0/1">Scott A. Hughes</a>
Bound orbits of black holes are very well understood. Given a Kerr black hole
of mass $M$ and spin $S = aM^2$, it is simple to characterize its orbits as
functions of the orbit’s geometry. How do the orbits change if the black hole
is itself evolving? How do the orbits change if the orbiting body evolves? 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,
or that changes the orbiting body’s mass. Provided this change happens slowly,
the orbit’s actions ($J_r, J_theta, J_phi$) 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 and in the orbiting body’s mass. We demonstrate the impact of
these results with several examples: how an orbit responds if accretion changes
a black hole’s mass and spin; how it responds if the orbiting body’s mass
changes due to accretion; and how the inspiral of a small body into a black
hole is affected by change to the hole’s mass and spin due to the gravitational
radiation absorbed by the event horizon. In all cases, the effect is very
small, but can be an order of magnitude or more larger than what was found in
previous work which did not take into account how the orbit responds due to
these effects.
Bound orbits of black holes are very well understood. Given a Kerr black hole
of mass $M$ and spin $S = aM^2$, it is simple to characterize its orbits as
functions of the orbit’s geometry. How do the orbits change if the black hole
is itself evolving? How do the orbits change if the orbiting body evolves? 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,
or that changes the orbiting body’s mass. Provided this change happens slowly,
the orbit’s actions ($J_r, J_theta, J_phi$) 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 and in the orbiting body’s mass. We demonstrate the impact of
these results with several examples: how an orbit responds if accretion changes
a black hole’s mass and spin; how it responds if the orbiting body’s mass
changes due to accretion; and how the inspiral of a small body into a black
hole is affected by change to the hole’s mass and spin due to the gravitational
radiation absorbed by the event horizon. In all cases, the effect is very
small, but can be an order of magnitude or more larger than what was found in
previous work which did not take into account how the orbit responds due to
these effects.
http://arxiv.org/icons/sfx.gif
