We investigated black hole evolution on a quantum-gravitational scattering framework with the aim of tackling the black hole information paradox. With this setup, various pieces of system information are explicit from the start and unitary evolution is manifest throughout. The scattering amplitudes factorize into a perturbative part and a non-perturbative part. The non-perturbative part is dominated by an instanton-type contribution, i.e. a black hole analogue of the Coleman–De Luccia bounce solution, and we propose that the Hawking radiation be identified with the particles generated by the vacuum decay. Our results indicate that the black hole degrees of freedom are entangled not only with the Hawking modes but also with the pre-Hawking modes. The Wald’s entropy charge measures their entanglement. The full quantum-gravitational entropy is defined as the vacuum expectation value of the Wald entropy charge. With this definition, a shifted Page-like curve is generically generated and its quantum extension is readily defined.

中文翻译：

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量子引力框架中的黑洞演化

我们在量子引力散射框架上研究了黑洞演化，旨在解决黑洞信息悖论。有了这种设置，各种系统信息从一开始就很明确，统一的演化贯穿始终。散射幅度分解为微扰部分和非微扰部分。非微扰部分主要是瞬时型贡献，即 Coleman-De Luccia 反弹解的黑洞模拟，我们建议将霍金辐射与真空衰变产生的粒子识别。我们的结果表明，黑洞的自由度不仅与霍金模式纠缠在一起，而且还与霍金前模式纠缠在一起。Wald 的熵电荷测量它们的纠缠。全量子引力熵定义为 Wald 熵电荷的真空期望值。有了这个定义，一般会生成一个移动的 Page 状曲线，并且它的量子扩展很容易定义。