We compute the spectra and total fluxes of quantum mechanically produced particles crossing the black hole and cosmological horizons in Schwarzschild de Sitter (SdS). Particle states are defined with respect to well-behaved, Kruskal coordinates near the horizons, and as a consequence we find that these spectra are generally non-thermal. The non-thermal Bogoliubov coefficient for a vacuum fluctuation near the black hole horizon to produce a particle that crosses the cosmological horizon is shown to equal to the convolution of two thermal coefficients, one at the cosmological temperature and one at the black hole temperature, weighted by the transmission coefficient for wave propagation in static SdS coordinates. In this sense virtual thermal propagation underlies the production process. This representation leads to the useful result that the geometric optics approximation is reliable when used together with a low frequency cut-off determined by the transmission coefficient. The large black hole limit is a quasi-equilibrium situation as both temperatures approach the common value of zero, the particle spectra become equal, and both emissions are exponentially suppressed. Small black holes radiate as thermal bodies and absorb a tiny flux of cosmological particles. The behavior of the quantum fluctuations on the horizons is seen to be consistent with the Schottky anomaly behavior of classical gravitational fluctuations.

中文翻译：

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Schwarzschild de Sitter 黑洞和宇宙粒子的产生

我们计算了穿越 Schwarzschild de Sitter (SdS) 黑洞和宇宙视界的量子力学产生的粒子的光谱和总通量。粒子状态是根据地平线附近表现良好的 Kruskal 坐标定义的，因此我们发现这些光谱通常是非热的。黑洞视界附近真空涨落产生穿过宇宙视界的粒子的非热 Bogoliubov 系数被证明等于两个热系数的卷积，一个在宇宙温度下，一个在黑洞温度下，加权通过静态 SdS 坐标中波传播的传输系数。从这个意义上说，虚拟热传播是生产过程的基础。这种表示导致有用的结果，即几何光学近似与由透射系数确定的低频截止一起使用时是可靠的。大黑洞极限是一种准平衡情况，因为两个温度都接近零的共同值，粒子光谱变得相等，并且两个发射都被指数抑制。小黑洞以热体的形式辐射并吸收微小的宇宙粒子流。视界上的量子涨落行为被认为与经典引力涨落的肖特基异常行为一致。大黑洞极限是一种准平衡情况，因为两个温度都接近零的共同值，粒子光谱变得相等，并且两个发射都被指数抑制。小黑洞以热体的形式辐射并吸收微小的宇宙粒子流。视界上的量子涨落行为被认为与经典引力涨落的肖特基异常行为一致。大黑洞极限是一种准平衡情况，因为两个温度都接近零的共同值，粒子光谱变得相等，并且两个发射都被指数抑制。小黑洞以热体的形式辐射并吸收微小的宇宙粒子流。视界上的量子涨落行为被认为与经典引力涨落的肖特基异常行为一致。