We investigate the evaporation process of a Kerr–de Sitter black hole with the Unruh–Hawking-like vacuum state, which is a realistic vacuum state modelling the evaporation process of a black hole originating from gravitational collapse. We also compute the greybody factors for gravitons, photons, and conformal-coupling massless scalar particles by using the analytic solutions of the Teukolsky equation in the Kerr–de Sitter background. It turns out that the cosmological constant quenches the amplification factor and it approaches to zero towards the critical point where the Nariai and extremal limits merge together. We confirm that even near the critical point, the superradiance of gravitons is more significant than that of photons and scalar particles. Angular momentum is carried out by particles several times faster than the mass energy decreases. This means that a Kerr–de Sitter black hole rapidly spins down to a nearly Schwarzschild–de Sitter black hole before it completely evaporates. We also compute the time evolution of the Bekenstein–Hawking entropy. The total entropy of the Kerr–de Sitter black hole and cosmological horizon increases with time, which is consistent with the generalized second law of thermodynamics.

我们研究了具有类似 Unruh-Hawking 真空状态的 Kerr-de Sitter 黑洞的蒸发过程，这是一种真实的真空状态，模拟了源自引力坍缩的黑洞蒸发过程。我们还使用 Kerr-de Sitter 背景中 Teukolsky 方程的解析解来计算引力子、光子和共形耦合无质量标量粒子的灰体因子。事实证明，宇宙常数会抑制放大因子，并且它在接近 Nariai 和极值极限合并在一起的临界点时趋近于零。我们证实，即使在临界点附近，引力子的超辐射也比光子和标量粒子的超辐射更显着。粒子产生角动量的速度比质量能量减少的速度快几倍。这意味着克尔-德西特黑洞在完全蒸发之前会迅速自旋下降到接近施瓦西-德西特的黑洞。我们还计算了 Bekenstein-Hawking 熵的时间演化。克尔-德西特黑洞和宇宙视界的总熵随时间增加，这与广义热力学第二定律是一致的。