标题： 自旋1在黑洞蒸发中的振幅 显示英文标题

标题： Spin-1 Amplitudes in Black-Hole Evaporation

摘要： 我们之前关于黑洞蒸发中标量场的量子振幅的研究，继引力坍缩之后，现在扩展到了麦克斯韦理论。 初始和最终的时空超曲面$\Sigma_{I,F}$上指定了边界数据，它们之间由一个大的洛伦兹固有时间隔$T$分隔，该时间在空间无穷远处测量。 初始边界数据可以被选择（例如）为球对称的，对应于引力坍缩之前的近似球形配置。 最终数据包括限制在$\Sigma_F$上的内在三维度规和标量场，以及自旋-1数据，自然地取为$\Sigma_{I,F} (i=1,2,3)$上的磁场$B_i$。 对于局部超对称理论，量子振幅应与$\exp(iS_{\rm class})$成正比，除了当边界数据中的频率远小于普朗克尺度时，修正项非常小。 在这里，$S_{\rm class}$是经典解的作用量。 洛伦兹振幅是通过取$\theta\to 0_+$的极限得到的。 通过类似于自旋-0情况中使用的方法，可以得到光子数据在$\Sigma_F$上的量子振幅。 磁边界条件通过超对称性与自然的自旋-2（引力波）边界条件相关，这些条件涉及固定Weyl张量的磁部分。 显示英文摘要

摘要： Our earlier work on the quantum amplitude for a scalar field in black-hole evaporation, following gravitational collapse, is here extended to Maxwell theory. Boundary data are specified on initial and final space-like hypersurfaces $\Sigma_{I,F}$, separated by a large Lorentzian proper-time interval $T$, as measured at spatial infinity. The initial boundary data may be chosen (say) to be spherically symmetric, corresponding to a nearly-spherical configuration prior to gravitational collapse. The final data include the intrinsic 3-metric and scalar field, restricted to $\Sigma_F$, in addition to spin-1 data, naturally taken to be the magnetic field $B_i$ on $\Sigma_{I,F} (i=1,2,3)$. For a locally-supersymmetric theory, the quantum amplitude should be proportional to $\exp(iS_{\rm class})$, apart from corrections which are very small when the frequencies in the boundary data are small compared to the Planck scale. Here, $S_{\rm class}$ is the action of the classical solution. The Lorentzian amplitude is found by taking the limit $\theta\to 0_+$. By a method similar to that used in the spin-0 case, one obtains the quantum amplitude for photon data on $\Sigma_F$. The magnetic boundary conditions are related by supersymmetry to the natural spin-2 (gravitational-wave) boundary conditions, which involve fixing the magnetic part of the Weyl tensor.