Massless Dirac particles in the vacuum C-metric
Massless Dirac particles in the vacuum C-metric
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DOI：
10.1088/0264-9381/32/21/215010
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发表时间：
2015-09
影响因子：
3.5
通讯作者：
D. Bini;E. Bittencourt;A. Geralico
中科院分区：
文献类型：
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作者：
D. Bini;E. Bittencourt;A. Geralico
我们研究真空 C 度量时空中无质量狄拉克粒子的行为，代表史瓦西黑洞解和与均匀加速观察者相关的林德勒平坦时空的非线性叠加。在某些条件下，C度量可以被认为是一个独特的实验室，用于测试粒子和场的固有属性与完整（精确）强场状态下的背景加速度之间的耦合。狄拉克方程可以通过使用例如类球坐标系来分离，从而将问题简化为一维径向和角度部分。径向方程和角度方程都可以用一般 Heun 函数精确求解。我们还提供了适当定义的加速度参数中的一阶扰动解，并计算了对粒子吸收率以及低频极限下相关散射问题的角平均横截面的加速度引起的校正。此外，我们表明，通过识别这些“加速度”谐波和克尔球谐波之间的映射，可以将角度特征值问题与克尔时空的类似问题一一对应。最后，在这方面，我们与众所周知的克尔自旋旋转耦合相比，讨论了本征自旋和时空加速度之间耦合的本质。
We study the behavior of massless Dirac particles in the vacuum C-metric spacetime, representing the nonlinear superposition of the Schwarzschild black hole solution and the Rindler flat spacetime associated with uniformly accelerated observers. Under certain conditions, the C-metric can be considered as a unique laboratory to test the coupling between intrinsic properties of particles and fields with the background acceleration in the full (exact) strong-field regime. The Dirac equation is separable by using, e.g., a spherical-like coordinate system, reducing the problem to one-dimensional radial and angular parts. Both radial and angular equations can be solved exactly in terms of general Heun functions. We also provide perturbative solutions to first order in a suitably defined acceleration parameter, and compute the acceleration-induced corrections to the particle absorption rate as well as to the angle-averaged cross section of the associated scattering problem in the low-frequency limit. Furthermore, we show that the angular eigenvalue problem can be put in one-to-one correspondence with the analogous problem for a Kerr spacetime, by identifying a map between these ‘acceleration’ harmonics and Kerr spheroidal harmonics. Finally, in this respect we discuss the nature of the coupling between intrinsic spin and spacetime acceleration in comparison with the well known Kerr spin-rotation coupling.