The Sachdev-Ye-Kitaev (SYK) model can be used to describe black holes (BHs) in two-dimensional nearly-Anti-de-Sitter gravity. We show that when such BHs are perturbed by a time-dependent negativeenergy perturbation, their interior can be partially revealed. In the SYK model, a partial measurement of the state of the Majorana fermion pairs allows one to construct a matching time-dependent negativeenergy perturbation of the BH geometry that shifts the state of the BH away from its equilibrium state. Kourkoulou and Maldacena showed that, if the perturbation is strong enough, the interior can be fully exposed and the BH disappears. Here, we show that when the perturbation is weaker than the threshold for full exposure, it effectively moves the horizon of the BH inwards, thus partially exposing the interior of the BH and leaving behind a smaller BH. The exposure is in proportion to the number of measured Majorana pairs and so also in proportion to the magnitude of the energy of the perturbation. From the boundary, the partial measurement is perceived as a burst of radiation whose strength and duration are proportional to the number of measured Majorana pairs. arXiv:1804.09017v3 [hep-th] 1 Apr 2019

We show that the state of the Hawking radiation emitted from a large Schwarzschild black hole (BH) deviates significantly from a classical state, in spite of its apparent thermal nature. For this state, the occupation numbers of single modes of massless asymptotic fields, such as photons, gravitons and possibly neutrinos, are small and, as a result, their relative fluctuations are large. The occupation numbers of massive fields are much smaller and suppressed beyond even the expected Boltzmann suppression. It follows that this type of thermal state cannot be viewed as classical or even semiclassical. We substantiate this claim by showing that, in a state with low occupation numbers, physical observables have large quantum fluctuations and, as such, cannot be faithfully described by a mean-field or by a WKB-like semiclassical state. Since the evolution of the BH is unitary, our results imply that the state of the BH interior must also be non-classical when described in terms of the asymptotic fields. We show that such a non-classical interior cannot be described in terms of a semiclassical geometry, even though the average curvature is sub-Planckian.

We discuss interacting, closed, bosonic and superstrings in thermal equilibrium at temperatures close to the Hagedorn temperature in flat space. We calculate S-matrix elements of the strings at the Hagedorn temperature and use them to construct a low-energy effective action for interacting strings near the Hagedorn temperature. We show, in particular, that the four-point amplitude of massless winding modes leads to a positive quartic interaction. Furthermore, the effective field theory has a generalized conformal structure, namely, it is conformally invariant when the temperature is assigned an appropriate scaling dimension. Then, we show that the equations of motion resulting from the effective action possess a winding-mode-condensate background solution above the Hagedorn temperature and present a worldsheet conformal field theory, similar to a Sine-Gordon theory, that corresponds to this solution. We find that the Hagedorn phase transition in our setup is second order, in contrast to a first-order transition that was found previously in different setups.

We calculate the entropy of an asymptotically Schwarzschild black hole, using an effective field theory of winding modes in type II string theory. In Euclidean signature, the geometry of the black hole contains a thermal cycle which shrinks towards the horizon. The light excitations thus include, in addition to the metric and the dilaton, also the winding modes around this cycle. The winding modes condense in the near-horizon region and source the geometry of the thermal cycle. Using the effective field theory action and standard thermodynamic relations, we show that the entropy, which is also sourced by the winding modes condensate, is exactly equal to the Bekenstein-Hawking entropy of the black hole. We then discuss some properties of the winding mode condensate and end with an application of our method to an asymptotically linear-dilaton black hole.

We consider the backreaction of the winding condensate on the cigar background. We focus on the case of the SL(2, ℝ)k/U(1) cigar associated with, e.g., the near-horizon limit of k NS5 black-branes. We solve the equations of motion numerically in the large k limit as a function of the amplitude, A, of the winding mode at infinity. We find that there is a critical amplitude, Ac = exp(−γ/2), that admits a critical solution. In string theory, the exact SL(2, ℝ)k/U(1) cigar CFT fixes completely the winding amplitude, As, at infinity. We find that in the large k limit there is an exact agreement, Ac = As. The critical solution is a cigar with a puncture at its tip; consequently, the black-hole entropy is carried entirely by the winding condensate. We argue that, in the Lorentzian case, the information escapes the black hole through this puncture.