论文标题
部分可观测时空混沌系统的无模型预测
Cosmological Magnetic Fields from Primordial Kerr-Newman Black Holes
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
The origin of our universe's cosmological magnetic fields remains a mystery. In this study, we consider whether these magnetic fields could have been generated in the early universe by a population of charged, spinning primordial black holes. To this end, we calculate the strength and correlation length of the magnetic fields generated by this population, and describe their evolution up to the current epoch. We find that near-extremal black holes in the mass range $ M \sim 10^{28} -10^{36} \, {\rm g}$ could potentially generate magnetic fields with present day values as large as $B \sim 10^{-20} - 10^{-15} \, {\rm G}$; those with $M \gtrsim10^{38} \, \rm{g}$ could have produced even larger fields $B \gtrsim 10^{-14} \, {\rm G}$. To motivate this scenario, we briefly discuss how new physics may have induced a chemical potential which could have briefly maintained the black holes in an electrically charged state in the early universe. Finally, we comment on a correlation between the parameters of the cosmological magnetic field and the stochastic gravitational wave background coming from the merger of primordial black hole binaries as the primary observable signature of this scenario.