Cosmic black-hole hair growth and quasar OJ287
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abstract
An old result ({\tt astro-ph/9905303}) by Jacobson implies that a black hole
with Schwarzschild radius $r_s$ acquires scalar hair, $Q \propto r_s^2 \mu$,
when the (canonically normalized) scalar field in question is slowly
time-dependent far from the black hole, $\partial_t \phi \simeq \mu M_p$ with
$\mu r_s \ll 1$ time-independent. Such a time dependence could arise in
scalar-tensor theories either from cosmological evolution, or due to the slow
motion of the black hole within an asymptotic spatial gradient in the scalar
field. Most remarkably, the amount of scalar hair so induced is independent of
the strength with which the scalar couples to matter. We argue that Jacobson's
Miracle Hair-Growth Formula${}^\copyright$ implies, in particular, that an
orbiting pair of black holes can radiate {\em dipole} radiation, provided only
that the two black holes have different masses. Quasar OJ 287, situated at
redshift $z \simeq 0.306$, has been argued to be a double black-hole binary
system of this type, whose orbital decay recently has been indirectly measured
and found to agree with the predictions of General Relativity to within 6%. We
argue that the absence of observable scalar dipole radiation in this system
yields the remarkable bound $|\,\mu| < (16 \, \hbox{days})^{-1}$ on the
instantaneous time derivative at this redshift (as opposed to constraining an
average field difference, $\Delta \phi$, over cosmological times), provided
only that the scalar is light enough to be radiated --- i.e. $m \lsim 10^{-23}$
eV --- independent of how the scalar couples to matter. This can also be
interpreted as constraining (in a more model-dependent way) the binary's motion
relative to any spatial variation of the scalar field within its immediate
vicinity within its host galaxy.
