Bound states of the Dirac equation on Kerr spacetime
Bound states of the Dirac equation on Kerr spacetime
复制标题
DOI：
10.1088/0264-9381/32/18/184001
复制
发表时间：
2015-09-24
影响因子：
3.5
通讯作者：
Dempsey, David
中科院分区：
文献类型：
--
作者：
Dolan, Sam R.;Dempsey, David
我们建立了旋转黑洞时空中质量中性自旋半粒子的狄拉克方程，并考虑了它的(准)束缚态：在未来视界内规则的引力囚禁模。由于(单粒子)Dirac场中没有超辐射，这些束缚态随时间衰减。我们介绍了一种实用的计算能级谱和衰减率的方法，并将我们的数值结果与已知的在小Mmu区和大Mmu区的渐近结果进行了比较。将微扰理论应用于贯穿视界的坐标系中，计算了能谱的精细结构，并与数值结果进行了比较，结果吻合较好。我们得到了由于黑洞旋转而产生的超精细分裂的数据。我们在时间域中发展了一般的初始数据，并展示了狄拉克束缚态在功率谱中是如何以谱线的形式出现的。在快速旋转区，我们发现在(玻色子)超辐射区低频共旋模的衰变被抑制。最后，我们讨论了物理影响和进一步工作的途径。
We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi) bound states: gravitationally-trapped modes which are regular across the future event horizon. These bound states decay with time, due to the absence of superradiance in the (single-particle) Dirac field. We introduce a practical method for computing the spectrum of energy levels and decay rates, and we compare our numerical results with known asymptotic results in the small-M mu and large-M mu regimes. By applying perturbation theory in a horizon-penetrating coordinate system, we compute the 'fine structure' of the energy spectrum and find good agreement with numerical results. We obtain data for a hyperfine splitting due to black hole rotation. We evolve generic initial data in the time domain, and show how Dirac bound states appear as spectral lines in the power spectra. In the rapidly-rotating regime, we find that the decay of low-frequency co-rotating modes is suppressed in the (bosonic) superradiant regime. We conclude with a discussion of physical implications and avenues for further work.