We study the semi-classical thermodynamics of two-dimensional de Sitter space (dS₂) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of Brown and York to dS₂, where a timelike boundary is introduced in the static patch to uniquely define conserved charges, including quasi-local energy. The boundary divides the static patch into two systems, a cosmological system and a black hole system, the former being unstable under thermal fluctuations while the latter is stable. A semi-classical quasi-local first law is derived, where the Gibbons–Hawking entropy is replaced by the generalized entropy. In the microcanonical ensemble the generalized entropy is stationary. Further, we show the on-shell Euclidean microcanonical action of a causal diamond in semi-classical JT gravity equals minus the generalized entropy of the diamond, hence extremization of the entropy follows from minimizing the action. Thus, we provide a first principles derivation of the island rule for U(1) symmetric dS₂ backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.

We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at $$ \mathcal{I} $$I ⁺ and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the past cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at $$ \mathcal{I} $$I ⁺ naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer will see unitary evaporation.

We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS₃ in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.

We describe holographic properties of near-AdS${}_2$ spacetimes that arise within spherically symmetric configurations of $\mathcal{N}=2$ 4D $U{\left(1\right)}^4$ supergravity for both gauged and ungauged theories. These theories pose a rich space of AdS${}_2\times S^2$ backgrounds, and their responses in the near-AdS${}_2$ region are not universal. In particular, we show that the spectrum of operators is dual to the matter fields, and their cubic interactions are sensitive to properties of the background and the theory it is embedded in. The properties that have the most striking effect are whether the background is supersymmetric or not and if the theory is gauged or ungauged. Interesting effects are due to the appearance of operators with $\Delta <2$, which depending on the background, can lead to, for instance, instabilities or extremal correlators. The resulting differences will have an imprint on the quantum nature of the microstates of near-extremal black holes, reflecting that not all extremal black holes respond equally when kicked away from extremality.

A bstract: We formulate and take two large strides towards proving a quantum version of the weak cosmic censorship conjecture. We first prove “Cryptographic Censorship”: a theorem showing that when the time evolution operator of a holographic CFT is approximately pseudorandom (or Haar random) on some code subspace, then there must be an event horizon in the corresponding bulk dual. This result provides a general condition that guarantees (in finite time) event horizon formation, with minimal assumptions about the global spacetime structure. Our theorem relies on an extension of a recent quantum learning no-go theorem and is proved using new techniques of pseudorandom measure concentration. To apply this result to cosmic censorship, we separate singularities into classical, semi-Planckian, and Planckian types. We illustrate that classical and semi-Planckian singularities are compatible with approximately pseudorandom CFT time evolution; thus, if such singularities are indeed approximately pseudorandom, by Cryptographic Censorship, they cannot exist in the absence of event horizons. This result provides a sufficient condition guaranteeing that seminal holographic results on quantum chaos and thermalization, whose general applicability relies on typicality of horizons, will not be invalidated by the formation of naked singularities in AdS/CFT.

A bstract: We quantify how the two-point function of a real scalar field is affected by the distortion caused by deforming AdS ₂ to a near-AdS ₂ background. At tree-level, the backreaction of the geometry induces a finite-temperature correction to the correlator that arises from interactions that the background generates. For a massive field, we show that this correction is not captured by JT gravity coupled to matter: it requires a backreaction of the metric field. For a massless field, the correction is controlled solely by the dilaton and hence is model-independent. We compare our findings with correlation functions on BTZ and find perfect agreement. We use our results to quantify the corrections for a class of correlators relevant to five- and four-dimensional black holes. We discuss how these corrections would enter in a holographic description of near-AdS ₂ ; we also comment on how these corrections provide a universal prediction for quasinormal modes in higher dimensions.