arXiv subjects

Ahmed Almheiri

Publications and source records attributed to Ahmed Almheiri.

At least 19 recordsLinked to original sources

arXiv2026

Continuing past the inner horizon using WKB

Features of the black hole interior can be extracted from the analytic structure of boundary correlation functions. Working in the geodesic approximation, we find analytic continuations that probe the interior of rotating and charged black holes. These generate contributions from timelike geodesics that thread the interior and emerge in a future universe. We implement these continuations on the momentum space two-point function and exemplify this in several black hole backgrounds. We also identify position space analytic continuations achieving the same task that incorporate different continued momentum space correlators. These correspond to non-perturbative corrections to the WKB approximation. We demonstrate this explicitly in the rotating BTZ black hole by showing that the interior geodesics contribute to the continued position space correlator and motivate a picture for how these contributions arise in higher dimensions. For AdS Schwarzschild, we identify the analytically continued solution that captures the bouncing geodesic. We discuss the possibility of using these continuations to probe the instability of inner horizons from the boundary.

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arXiv2025

Holography on the Quantum Disk

Motivated by recent study of DSSYK and the non-commutative nature of its bulk dual, we review and analyze an example of a non-commutative spacetime known as the quantum disk proposed by L. Vaksman. The quantum disk is defined as the space whose isometries are generated by the quantum algebra $U_q(\mathfrak{su}_{1,1})$. We review how this algebra is defined and its associated group $SU_q(1,1)$ that it generates, highlighting its non-trivial coproduct that sources bulk non-commutativity. We analyze the structure of holography on the quantum disk and study the imprint of non-commutativity on the putative boundary dual.

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arXiv2025

$T\overline{T}$ and the black hole interior

There is ample evidence that the bulk dual of a $T\overline{T}$ deformed holographic CFT is a gravitational system with a finite area cutoff boundary. For states dual to black holes, the finite cutoff surface cannot be moved beyond the event horizon. We overcome this by considering an extension of the $T\overline{T}$ deformation with a boundary cosmological constant and a prescription for a sequence of flows that successfully pushes the cutoff boundary past the event horizon and arbitrarily close to the black hole singularity. We show how this sequence avoids the complexification of the deformed boundary energies. The approach to the singularity is reflected on the boundary by the approach of the deformed energies to an accumulation point in the limit of arbitrarily large distance in deformation space. We argue that this sequence of flows is automatically implemented by the gravitational path integral given only the values of the initial ADM charges and the area of the finite cutoff surface, suggesting a similar automatic boundary mechanism that keeps all the deformed energies real at arbitrary values of the deformation parameter. This leads to a natural definition of a deformed boundary canonical ensemble partition function that sums over the entire spectrum and remains real for any value of the deformation parameter. We find that this partition function displays Hagedorn growth at the scale set by the deformation parameter, which we associate to the region near the inner horizon in the bulk dual.

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arXiv2025

Measurements $\mathit{with}$ probabilities in the final state proposal

Bousso and Stanford (BS) argued that the black hole final state proposal leads to acausal effects and ill-defined probabilities for the AMPS experiment. We identify a loophole in their analysis using insights from entanglement wedge reconstruction and replica wormholes. We trace the cause of the BS problems to the misidentification of the physical interior where the second AMPS measurement happens from among the multiple interiors introduced by the first measurement.

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arXiv2024

Quantum gravity of the Heisenberg algebra

We consider a simplified model of double scaled SYK (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory in its own right. We study properties of the emergent geometry including its dynamics in response to inserting matter particles. In particular, we find that the model displays de Sitter-like properties such as that infalling matter reduces the rate of growth of geodesic slices between the two boundaries. The simplicity of the model allows us to compute the full generating functional for correlation functions of the length mode or any number of matter operators. We provide evidence that the effective action of the geodesic length between boundary points is non-local. Furthermore, we use the on-shell solution for the geodesic lengths between any two boundary points to reconstruct an effective bulk metric and reverse engineer the dilaton gravity theory that generates this metric as a solution.

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arXiv2023

Islands outside the horizon

We consider an AdS$_2$ black hole in equilibrium with a bath, which we take to have a dual description as (0+1)-dimensional quantum mechanical system coupled to a (1+1)-dimensional field theory serving as the bath. We compute the entropies of both the quantum mechanical degrees of freedom and of the bath separately, while allowing contributions from entanglement wedge "islands". We find situations where the island extends {\it outside} the black hole horizon. This suggests possible causality paradoxes which we show are avoided because of the quantum focusing conjecture. Finally, we formulate a version of the information paradox for a black hole in contact with a bath in the Hartle-Hawking state, and demonstrate the role of islands in resolving this paradox.

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arXiv2022

The Entanglement Wedge of Unknown Couplings

The black hole interior is a mysterious region of spacetime where non-perturbative effects are sometimes important. These non-perturbative effects are believed to be highly theory-dependent. We sharpen these statements by considering a setup where the state of the black hole is in a superposition of states corresponding to boundary theories with different couplings, entangled with a reference which keeps track of those couplings. The entanglement wedge of the reference can then be interpreted as the bulk region most sensitive to the values of the couplings. In simple bulk models, e.g., JT gravity + a matter BCFT, the QES formula implies that the reference contains the black hole interior at late times. We also analyze the Renyi-2 entropy of the reference, which can be viewed as a diagnostic of chaos via the Loschmidt echo. We find explicitly the replica wormhole that diagnoses the island and restores unitarity. Numerical and analytical evidence of these statements in the SYK model is presented. Similar considerations are expected to apply in higher dimensional AdS/CFT, for marginal and even irrelevant couplings.

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arXiv2020

The entropy of Hawking radiation

In this review, we describe recent progress on the black hole information problem that involves a new understanding of how to calculate the entropy of Hawking radiation. We show how the method for computing gravitational fine-grained entropy, developed over the past 15 years, can be extended to capture the entropy of Hawking radiation. This technique reveals large corrections needed for the entropy to be consistent with unitary black hole evaporation.

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arXiv2020

Entanglement islands in higher dimensions

It has been suggested in recent work that the Page curve of Hawking radiation can be recovered using computations in semi-classical gravity provided one allows for "islands" in the gravity region of quantum systems coupled to gravity. The explicit computations so far have been restricted to black holes in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically construct a five-dimensional asymptotically AdS geometry whose boundary realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole in equilibrium with a bath. We also numerically find two types of extremal surfaces: ones that correspond to having or not having an island. The version of the information paradox involving the eternal black hole exists in this setup, and it is avoided by the presence of islands. Thus, recent computations exhibiting islands in two-dimensional gravity generalize to higher dimensions as well.

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arXiv2020

Replica Wormholes and the Entropy of Hawking Radiation

The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number $n \to 1$, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these replica wormholes explicitly in two-dimensional Jackiw-Teitelboim gravity coupled to matter.

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arXiv2019

Universal Constraints on Energy Flow and SYK Thermalization

We study the dynamics of a quantum system in thermal equilibrium that is suddenly coupled to a bath at a different temperature, a situation inspired by a particular black hole evaporation protocol. We prove a universal positivity bound on the integrated rate of change of the system energy which holds perturbatively in the system-bath coupling. Applied to holographic systems, this bound implies a particular instance of the averaged null energy condition. We also study in detail the particular case of two coupled SYK models in the limit of many fermions using the Schwinger-Keldysh non-equilibrium formalism. We solve the resulting Kadanoff-Baym equations both numerically and analytically in various limits. In particular, by going to low temperature, this setup enables a detailed study of the evaporation of black holes in JT gravity.

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arXiv2019

The Page curve of Hawking radiation from semiclassical geometry

We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for "islands" in determining the entanglement wedge.

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arXiv2019

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

Bulk quantum fields are often said to contribute to the generalized entropy $\frac{A}{4G_N} +S_{\mathrm{bulk}}$ only at $O(1)$. Nonetheless, in the context of evaporating black holes, $O(1/G_N)$ gradients in $S_{\mathrm{bulk}}$ can arise due to large boosts, introducing a quantum extremal surface far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary $2d$ bulk system defined by Jackiw-Teitelboim gravity coupled to a 1+1 CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time $\fracβ{2π} \ln ΔS + O(1)$ in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process.

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arXiv2018

Holographic Quantum Error Correction and the Projected Black Hole Interior

The quantum error correction interpretation of AdS/CFT establishes a sense of fluidity to the bulk/boundary dictionary. We show how this property can be utilized to construct a dictionary for operators behind horizons of pure black holes. We demonstrate this within the context of the SYK model with pure black hole microstates obtained via projecting out a single side of the thermofield double (and perturbed versions thereof). Assuming an erasure subsystem code for the duality between the eternal black hole and the thermofield double, this projection results in a rewiring of the dictionary so as to map the interior operators to the remaining boundary in a determinable way. We find this dictionary to be sensitive to the implemented projection in a manner reminiscent of previous state-dependent constructions of the black hole interior. We also comment on how the fluidity of the dictionary can be used to transfer information between two black holes connected by a wormhole, relating the ideas of entanglement wedge reconstruction and the Hayden-Preskill decoding criterion.

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arXiv2018

Escaping the Interiors of Pure Boundary-State Black Holes

We consider a class of pure black hole microstates and demonstrate that they can be made escapable by turning on certain double trace deformations in the CFT. These microstates are dual to BCFT states prepared via a Euclidean path integral starting from a boundary in Euclidean time. These states are dual to black holes in the bulk with an End-of-the-World brane; a codimension one timelike boundary of the spacetime behind the horizon. We show that by tuning the sign of the coupling of the double trace operator to the boundary conditions on the brane the deformation injects negative energy into the black hole causing a time advance for signals behind the horizon. We demonstrate how the property of escapability in the considered microstates follows immediately from the traversability of deformed wormholes. We briefly comment on reconstruction of the black hole interior and state dependence.

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arXiv2017

Inside Out: Meet The Operators Inside The Horizon

Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we study the reconstruction of operators behind causal horizons in time dependent geometries obtained by acting with shockwaves on pure states or thermal states. These geometries admit a natural basis of gauge invariant operators, namely those geodesically dressed to the boundary along geodesics which emanate from the bifurcate horizon at constant Rindler time. We outline a procedure for obtaining operators behind the causal horizon but inside the entanglement wedge by exploiting the equality between bulk and boundary time evolution, as well as the freedom to consider the operators evolved by distinct Hamiltonians. This requires we carefully keep track of how the operators are gravitationally dressed and that we address issues regarding background dependence. We compare this procedure to reconstruction using modular flow, and illustrate some formal points in simple cases such as AdS$_2$ and AdS$_3$.

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arXiv2017

Linearity of Holographic Entanglement Entropy

We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.

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arXiv2016

Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes

It has been argued recently by Almheiri and Polchinski that the near-horizon conformal symmetry of extremal black holes must be broken due to gravitational backreaction at an IR scale linear in $G_N$. In this paper, we show that this scale coincides with the so-called `thermodynamic mass gap' of near-extremal black holes, a scale which signals the breakdown of their thermodynamic description. We also develop a method which extends the analysis of Almheiri and Polchinski to more complicated models with extremal throats by studying the bulk linearized quantum field theory. Moreover, we show how their original model correctly captures the universal physics of the near-horizon region of near-extremal black holes at tree level, and conclude that this equivalence of the conformal breaking and mass gap scale is general.

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