克尔黑洞对大质量矢量场的霍金辐射
Hawking emission of massive vector fields by Kerr black holes
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中文总结 AI 辅助
该研究首次计算克尔黑洞对大质量矢量场的霍金辐射谱，确定灰体因子及质量、自旋损失函数，分析极化模式贡献、蒸发率及超辐射发射等，揭示高自旋黑洞能在低温下发射大质量矢量场且超辐射更显著。
中文摘要 AI 辅助
我们首次计算了旋转克尔黑洞对大质量矢量（普罗卡）场的霍金辐射谱，确定了相关的灰体因子以及由此产生的质量和自旋损失函数。特别表明，普罗卡场的标量（纵向）极化在无质量极限下（此时成为纯规范模式）的谱接近自由标量场的谱，不过对于有限质量存在显著差异。两个矢量（横向）极化模式的贡献与佩奇在无质量极限下对麦克斯韦场得到的结果一致。对于缓慢旋转的黑洞，蒸发率由标量模式主导，而当黑洞接近极端时由两个矢量模式主导。对于霍金温度\(T_H\lesssim|\mu - \Omega_H|\)，普罗卡霍金辐射受玻尔兹曼抑制，其中\(\mu\)是场质量，\(\Omega_H\)是黑洞视界的角速度。这意味着高自旋黑洞能在参数低于场质量的温度下有效发射大质量矢量场。最后还发现，超辐射发射对于大质量矢量场更显著，最大放大因子约为\(7\%\)（无质量光子约为\(4\%\)）。
英文摘要
We compute, for the first time, the Hawking emission spectrum of massive vector (Proca) fields by spinning Kerr black holes, determining the associated greybody factors and the resulting mass and spin loss functions. We show, in particular, that the scalar (longitudinal) polarization of the Proca field has a spectrum approaching that of a free scalar field in the massless limit (in which it becomes a pure gauge mode), although we find substantial differences for finite mass. The contribution of the two vector (transverse) polarization modes coincides, as expected, with the one obtained by Page for the Maxwell field in the massless limit. The black hole's evaporation rate is dominated by the scalar mode for slowly spinning black holes and by the two vector modes as the black hole approaches extremality. As for other fields, we find that Proca Hawking emission is Boltzmann-suppressed for Hawking temperatures $T_H\lesssim |μ-Ω_H|$, where $μ$ is the field mass and $Ω_H$ is the angular velocity of the black hole's horizon. This implies that highly spinning black holes can efficiently emit massive vector fields at temperatures parametrically below the field's mass. Finally, we also find that superradiant emission is more pronounced for massive vector fields, with a maximum amplification factor of $\simeq 7\%$ (compared to $\simeq 4\%$ for massless photons).
