We consider the Hawking radiation emitted by an evaporating black hole in JT gravity and compute the entropy of arbitrary subsets of the radiation in the slow evaporation limit, and find a zoo of possible island saddles. The Hawking radiation is shown to have long range correlations. We compute the mutual information between early and late modes and bound from below their squashed entanglement. A small subset of late modes are shown to be correlated with modes in a suitably large subset of the radiation previously emitted as well as later modes. We show how there is a breakdown of the semi-classical approximation in the form of a violation of the Araki–Lieb triangle entropy inequality, if the interior of the black hole and the radiation are considered to be separate systems. Finally, we consider how much of the radiation must be collected, and how early, to recover information thrown into the black hole as it evaporates.

Computational complexity is a quantum information concept that recently has found applications in the holographic understanding of the black hole interior. We consider quantum computational complexity for $n$ qubits using Nielsen’s geometrical approach. In the definition of complexity there is a big amount of arbitrariness due to the choice of the penalty factors, which parametrizes the cost of the elementary computational gates. In order to reproduce desired features in holography, such as ergodicity and exponential maximal complexity for large number of qubits $n$, negative curvatures are required. With the simplest choice of penalties, this is achieved at the price of singular sectional curvatures in the large $n$ limit. We investigate a choice of penalties in which we can obtain negative curvatures in a smooth way. We also analyze the relation between operator and state complexities, framing the discussion with the language of Riemannian submersions. This provides a direct relation between geodesics and curvatures in the unitaries and the states spaces, which we also exploit to give a closed-form expression for the metric on the states in terms of the one for the operators. Finally, we study conjugate points for a large number of qubits in the unitary space and we provide a strong indication that maximal complexity scales exponentially with the number of qubits in a certain regime of the penalties space.

We classify AdS₃ solutions preserving $$ \mathcal{N} $$N = (8, 0) supersymmetry in ten and eleven dimensions and find the local form of each of them. These include the AdS₃×S⁶ solution of [1] and the embeddings of AdS₃ into AdS₄×S⁷, AdS₅×S⁵, AdS₇/ℤ_k×S⁴ and its IIA reduction within AdS₇. More interestingly we find solutions preserving the superconformal algebras $$ {\mathfrak{f}}_4,\mathfrak{su}\left(1,1|4\right),\mathfrak{osp}\left({4}^{\ast }|4\right) $$f 4 , su 1 1 4 , osp 4 ∗ 4 on certain squashings of the 7-sphere. These solutions asymptote to AdS₄×S⁷ and are promising candidates for holographic duals to defects in Chern-Simons matter theories.