Non-thermal radiation of black hole off canonical typicality

We study the Hawking radiation of black holes by considering the canonical typicality. For the universe consisting of black holes and their outer part, we directly obtain a non-thermal radiation spectrum of an arbitrary black hole from its entropy, which only depends on a few external qualities (known as hairs), such as mass, charge, and angular momentum. Our result shows that the spectrum of the non-thermal radiation is independent of the detailed quantum tunneling dynamics across black hole horizon. We prove that the black hole information paradox is naturally resolved by taking account the correlation between black hole and its radiation in our approach.Comment: 5 pages, 1 figure, pulished on Europhysics Letters, comments are welcome

Time-reversal of multiple-force-point chordal SLEκ(ρ‾)\mathrm{SLE}_\kappa(\underline{\rho})

Chordal SLE$_\kappa(\underline{\rho})$ is a natural variant of chordal SLE curve. It is a family of random non-crossing curves on the upper half plane from 0 to $\infty$, whose law is influenced by additional force points on $\mathbb R$. When there are force points away from the origin, the law of SLE$_\kappa(\underline{\rho})$ is not reversible as the ordinary chordal SLE$_\kappa$. Zhan (2019) give an explicit description of the law of the time reversal of SLE$_\kappa(\underline{\rho})$ when all force points lies on the same sides of the origin, and conjectured that a similar result holds in general. In this paper we prove his conjecture. In particular, based on Zhan's result, using the techniques from the Imaginary Geometry developed by Miller and Sheffield (2013), we show that when $\kappa\in(0,8)$, the law of the time reversal of non-boundary filling $\mathrm{SLE}_\kappa(\underline{\rho})$ process is absolutely continuous with respect to $\mathrm{SLE}_\kappa(\underline{\hat{\rho}})$ for some $\underline{\hat{\rho}}$ determined by $\underline{\rho}$, with the Radon-Nikodym derivative being a product of conformal derivatives.Comment: 13 pages, 6 figure