Grey-body factors, irreversibility and multiple island saddles

Abstract

We consider the effect of grey-body factors on the entanglement island prescription for computing the entropy of an arbitrary subset of the Hawking radiation of an evaporating black hole. When there is a non-trivial grey-body factor, the modes reflected back into the black hole affect the position of the quantum extremal surfaces at a subleading level with respect to the scrambling time. The grey-body factor allows us to analyse the role of irreversibility in the evaporation. In particular, we show that irreversibility allows multiple saddles to dominate the entropy, rather than just two as expected on the basis of Page’s theorem. We show that these multiple saddles can be derived from a generalization of Page’s theorem that involves a nested temporal sequence of unitary averages. We then consider how irreversibility affects the monogamy entanglement problem.

Black hole information recovery in JT gravity

“…A more accurate treatment of the problem would require introducing the greybody factor to take into account that the Hawking modes must tunnel through a potential barrier in order to reach I `. Following [19], we are restricting to the case where the greybody factor just depends on the frequency and the black-hole temperature, which is only true for the Schwarzschild case, where there is a single scale in the problem (the Schwarzschild radius), or JT gravity, where the greybody factor can be introduced by hand as a semi-reflective barrier between the gravity region and the bath. Given this assumption, the greybody factor is simply described by an overall coefficient ξ which controls the reversibility of the problem; in particular we have the following relation between the entropy flux of the black hole and the radiation:…”

“…In this section we set the greybody coefficient (introduced in (2.8)) ξ " 2. It is possible to relax this condition at the expense of a more complicated analysis: see [19].…”

“…The change in the map V ptq induced by D in (3. 19) suggests that we should introduce a new set of KS-type coordinates p Ũ , Ṽ q with an associated map…”