Paper detail

Cosmic Black-Hole Hair Growth and Quasar OJ287

An old result ({\tt astro-ph/9905303}) by Jacobson implies that a black hole with Schwarzschild radius $r_s$ acquires scalar hair, $Q \propto r_s^2 μ$, when the (canonically normalized) scalar field in question is slowly time-dependent far from the black hole, $\partial_t ϕ\simeq μM_p$ with $μr_s \ll 1$ 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${}^©$ 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 $|\,μ| < (16 \, \hbox{days})^{-1}$ on the instantaneous time derivative at this redshift (as opposed to constraining an average field difference, $Δϕ$, 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.