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arXiv 1111.4009gr-qcastro-ph.COhep-th
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宇宙黑洞头发生长与类星体OJ287

Cosmic Black-Hole Hair Growth and Quasar OJ287

M. W. Horbatsch, C. P. Burgess

摘要:

Jacobson的一个旧结果({\tt astro-ph/9905303})暗示,当(正则归一化的)标量场远离黑洞缓慢依赖于时间时,具有史瓦西半径$r_s$的黑洞获得标量头发$Q \propto r_s^2 μ$,$\partial_t ϕ\simeq μM_p$与$μr_s \ll 1$时间无关。在标量张量理论中,这种时间依赖性可能来自宇宙演化,或者是由于黑洞在标量场中的渐近空间梯度内的缓慢运动。最值得注意的是,如此诱导的标量毛发的数量与标量与物质耦合的强度无关。我们认为,雅各布森的奇迹头发生长公式${}^©$意味着,特别是,一个轨道上的黑洞对可以辐射{\em偶极子}辐射,只要这两个黑洞有不同的质量。类星体OJ 287位于$z \simeq 0.306$的红移处,被认为是一个双黑洞双星系统,其轨道衰减最近被间接测量,并发现与广义相对论的预测在6%以内。我们认为,在这个系统中没有可观察到的标量偶极辐射产生显着的约束$|\,μ| < (16 \, \hbox{days})^{-1}$的瞬时时间导数在这个红移(而不是约束平均场差,$Δϕ$,在宇宙学时间),只要标量是轻到足以被辐射-即$m \lsim 10^{-23}$ eV-独立的标量如何耦合到物质。这也可以被解释为(以一种更依赖于模型的方式)限制双星的运动相对于其宿主星系内紧邻的标量场的任何空间变化。

英文摘要:

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.

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