We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-003180.pdf

Black holes as mirrors: quantum information in random subsystems

Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations

Emergence of non-linear electrodynamic theories from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:math>-like deform

Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of the bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the anti--de Sitter-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system's parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator. 

Bath deformations, islands, and holographic complexity

We show that the recently introduced ModMax theory of electrodynamics
and its Born-Infeld-like generalization are related by a flow equation
driven by a quadratic combination of stress-energy tensors. The operator
associated to this flow is a 4d4d
analogue of the T\overline{T}TT¯
deformation in two dimensions. This result generalizes the observation
that the ordinary Born-Infeld Lagrangian is related to the free Maxwell
theory by a current-squared flow. As in that case, we show that no
analogous relationship holds in any other dimension besides
d=4d=4.
We also demonstrate that the \mathcal{N}=1𝒩=1
supersymmetric version of the ModMax-Born-Infeld theory obeys a related
supercurrent-squared flow which is formulated directly in
\mathcal{N} = 1𝒩=1
superspace.

On Current-Squared Flows and ModMax Theories

The relationship between thermodynamics and the Lloyd bound on the holographic complexity for a black hole has been of interest. We consider D dimensional anti-de Sitter black holes with hyperbolic geometry as well as black holes with momentum relaxation that have a minimum for temperature and mass. We show that the singular points of the thermodynamic curvature of the black holes, as thermodynamic systems, correspond to the zero points of the action and volume complexity at the Lloyd bound. For such black holes with a single horizon, the complexity of volume and the complexity of action at minimum mass and minimum temperature are zero, respectively. We show that the thermodynamic curvature diverges at these minimal values. Because of the behaviour of action complexity and thermodynamic curvature at minimum temperature, we propose the action complexity as an order parameter of the black holes as thermodynamic systems. Also, we derive the critical exponent related to the thermodynamic curvature in diﬀerent dimensions.

http://link.aps.org/pdf/10.1103/PhysRevD.106.024044

H. Babaei-Aghbolagh

Papers

Thermodynamic geometry and complexity of black holes in theories with broken translational invariance