AI 中文总结
研究黑洞在外部磁场中蒸发的电磁辐射，通过将霍金辐射近似为零流体外流，采用拉普拉斯变换确定辐射箭头，得出发射光谱能量红移为主且蒸发结束无明亮爆发的结论，还给出了经典类比。
AI 中文摘要
我们描述了一种经典（非量子）辐射过程：真空中黑洞在外部磁场中蒸发时的额外（相对于霍金辐射）辐射。该电磁辐射过程完全无电荷，与格特申施泰因 - 泽尔多维奇效应有相似之处。时空度规的时间演化扰动静态背景磁场，即使在没有物理电荷或电流的情况下也会诱导出一个辐射场作为有效电磁源。为分离时间相关时空对外部磁场的动态影响，我们将霍金辐射近似为受中心质量\(M(t)\)规定时间依赖性支配的零流体球对称外流。我们采用拉普拉斯变换，选择电磁响应的延迟出射分支，产生与\(\Theta(t - r)\)成比例的场，从而确定因果辐射发射箭头。发射的光谱能量以红移为主，标度为\(d\mathcal{E}_B/d\omega \propto B_0^2 m_0^2 \tau_H^{-2/3} \omega^{-8/3}\)，其中\(\tau_H\)是霍金蒸发时间尺度，对应纯横电（TE）模式。蒸发结束时没有最终的明亮爆发。我们为此机制提供了经典类比，如传输线发射以及具有随时间变化介电常数的介质中的位移电流发射。
英文摘要
We describe a classical (non-quantum) radiation process: additional (to Hawking) emission by a black hole evaporating in an external magnetic field in vacuum. The electromagnetic radiation process is completely electric charge-free and bears some resemblance to the Gertsenshtein-Zel'dovich effect. The time evolution of the spacetime metric perturbs a static background magnetic field, inducing a radiative field that acts as an effective electromagnetic source even in the absence of physical charges or currents. To isolate the dynamic effects of the time-dependent spacetime on the external magnetic field, we approximate Hawking radiation as a spherically symmetric outflow of null fluid governed by the prescribed time-dependence of the central mass $M(t)$. We employ Laplace transform, which selects the retarded outgoing branch of the electromagnetic response, producing fields proportional to $Θ(t-r)$ and thereby fixing a causal radiative arrow of emission. The emitted spectral energy is red-dominated, scaling as $d\mathcal{E}_B/dω\propto B_0^2 m_0^2 τ_H^{-2/3} ω^{-8/3}$, where $τ_H$ is the Hawking evaporation timescale, and corresponds to a pure Transverse Electric (TE) mode. There is no final bright burst at the end of the evaporation. We offer classical analogues for this mechanism as transmission-line emission and, separately, as the displacement current emission from a medium with time-varying dielectric permittivity.
Comments22 pages, 3 figures
