We construct an infinite family of microstates with geometric interiors for eternal black holes in general relativity a negative cosmological constant any dimension. Wormholes the Euclidean path integral gravity cause these states to have small, but nonzero, quantum mechanical overlaps that universal form. The dramatic consequence: span Hilbert space log dimension equal Bekenstein-Hawking entropy. semiclassical we contain Einstein-Rosen bridges arbitrary size behind their horizons. Our...

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions terms collapsing dust shells the hole interior. Quantum mechanical wormholes cause these states to exponentially small, but universal, overlaps. show that overlaps imply span a Hilbert space log dimension equal event horizon area divided by four times Newton constant, explaining statistical origin Bekenstein-Hawking entropy. Published American Physical Society 2024

A bstract The principle of maximum ignorance posits that the coarse-grained description a system is maximally agnostic about its underlying microscopic structure. We briefly review this for random matrix theory and eigenstate thermalization hypothesis. then apply in holography to construct ensembles mixed states. This leads an ensemble microstates which models our ignorance, on average reproduces effective semiclassical physics given bulk state. call state-averaging ansatz . output model...

We refine and extend a recent construction of sets black hole microstates with semiclassical interiors that span Hilbert space dimension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mi>S</a:mi></a:msup></a:math>, where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi></c:math> is the entropy. elaborate on definition properties in statistical mechanics. The gravitational description employs matter shells...

A bstract We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the BTZ hole, which encompasses in an exact manner effects of conformal fields with large central charge presence including backreaction to metric. Our results show Volume Complexity admits a consistent expansion and correctly reproduces known limits. On other hand, generalized Action picks up contributions singularity, modified due...

A bstract We construct higher dimensional Euclidean AdS wormhole solutions that reproduce the statistical description of correlation functions an ensemble heavy CFT operators. consider operator which effectively backreacts on geometry in form a thin shell dust particles. Assuming dynamical chaos ETH ansatz, we demonstrate semiclassical path integral provides effective microscopic features CFT. The provide microcanonical saddlepoint contributions to cumulants over finally elaborate role these...

A bstract We construct entangled microstates of a pair holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement two disconnected auxiliary spacetimes. show that island formula for fine grained entropy one follows from standard gravitational replica trick calculation. In generic settings, contained wedge CFTs. then...

We establish a version of the Momentum/Complexity (PC) duality between rate operator complexity growth and radial component bulk momentum for test system falling into black hole. In systems finite entropy, our map remains valid arbitrarily late times after scrambling. The asymptotic regime linear is associated to frozen in interior hole, measured with respect time foliation by extremal codimension-one surfaces which saturate without reaching singularity. detailed analysis this paper uses...

We show that the holographic Complexity = Volume proposal satisfies a very general notion of Momentum/Complexity correspondence (PC), based on Momentum Constraint General Relativity. It relates rate complexity variation with an appropriate matter momentum flux through spacelike extremal surfaces. This formalizes intuitive idea `gravitational clumpling' increases complexity, and required `infall momentum' is shown to have Newtonian avatar which expresses this idea. The proposed form PC found...

A bstract Holographic complexity, in the guise of Complexity = Volume prescription, comes equipped with a natural correspondence between its rate growth and average infall momentum matter bulk. This Momentum/Complexity can be related to an integrated version constraint general relativity. In this paper we propose generalization, using full Codazzi equations as starting point, which successfully accounts for purely gravitational contributions momentum. The proposed formula is explicitly...

We study the dynamical generation of randomness in Brownian systems as a function degree locality Hamiltonian. first express trace distance to unitary design for these terms an effective equilibrium thermal partition function, and provide set conditions that guarantee linear time design. relate spectral properties time-evolution operator. apply considerations p <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math> -SYK model . show is linear,...

We study the behavior of R\'enyi entropies for pure states from standard assumptions about chaos in high-energy spectrum Hamiltonian a many-body quantum system. compute exact long-time averages and show that noise around these values is exponentially suppressed microcanonical entropy. For delocalized over band, average approximately reproduces equilibration proposal H. Liu S. Vardhan, with extra structure arising at order non-planar permutations. analyze equilibrium approximation AdS/CFT...

A bstract We study the structure of entanglement wedges in Kasner-AdS geometry, which provides an example AdS/CFT engineered cosmological singularity. investigate specific limitations causal reconstruction methods, imposed by presence singularities, and we show supremacy modular reconstruction. This model where based on a proper operator subalgebra is more powerful than strongest possible reconstruction, complete algebra.

A bulge surface, on a time reflection-symmetric Cauchy slice of holographic spacetime, is non-minimal extremal surface that occurs between two locally minimal surfaces homologous to given boundary region. According the python's lunch conjecture Brown et al., bulge's area controls complexity bulk reconstruction, in sense amount post-selection needs be overcome for reconstruction entanglement wedge beyond outermost surface. We study geometry bulges variety classical spacetimes, and discover...

We refine and extend a recent construction of sets black hole microstates with semiclassical interiors that span Hilbert space dimension $e^S$, where $S$ is the entropy. elaborate on definition properties in statistical mechanics. The gravitational description employs matter shells interior hole, we argue limit are very heavy, acquires universal validity. To this end, show it for wide classes holes: first to rotating charged holes, including extremal near-extremal solutions, or without...

A bulge surface, on a time reflection-symmetric Cauchy slice of holographic spacetime, is non-minimal extremal surface that occurs between two locally minimal surfaces homologous to given boundary region. According the python’s lunch conjecture Brown et al., bulge’s area controls complexity bulk reconstruction, in sense amount post-selection needs be overcome for reconstruction entanglement wedge beyond outermost surface. We study geometry bulges variety classical spacetimes, and discover...

In this paper, we present a quantitative holographic relation between microscopic measure of randomness and the geometric length wormhole in black hole interior. To end, perturb an AdS with Brownian semiclassical sources, implementing continuous version random quantum circuit for hole. We use to prepare ensembles states whose duals contain Einstein-Rosen (ER) caterpillars: long cylindrical wormholes large numbers matter inhomogeneities, linearly growing time. setup, show semiclassically that...

We study the dynamical generation of randomness in Brownian systems as a function degree locality Hamiltonian. first express trace distance to unitary design for these terms an effective equilibrium thermal partition function, and provide set conditions that guarantee linear time design. relate spectral properties time-evolution operator. apply considerations $p$-SYK model $p$. show is linear, with slope proportional $1/p$. corroborate when $p$ order system size this reproduces behavior...

We construct entangled microstates of a pair holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement two disconnected auxiliary spacetimes. show that island formula for fine grained entropy one follows from standard gravitational replica trick calculation. In generic settings, contained wedge CFTs. then investigate...

The principle of maximum ignorance posits that the coarse-grained description a system is maximally agnostic about its underlying microscopic structure. We briefly review this for random matrix theory and eigenstate thermalization hypothesis. then apply in holography to construct ensembles mixed states. This leads an ensemble microstates which models our ignorance, on average reproduces effective semiclassical physics given bulk state. call state-averaging ansatz. output model prediction...

We construct higher dimensional Euclidean AdS wormhole solutions that reproduce the statistical description of correlation functions an ensemble heavy CFT operators. consider operator which effectively backreacts on geometry in form a thin shell dust particles. Assuming dynamical chaos ETH ansatz, we demonstrate semiclassical path integral provides effective microscopic features CFT. The provide microcanonical saddlepoint contributions to cumulants over finally elaborate role these wormholes...

We construct an infinite family of microstates with geometric interiors for eternal black holes in general relativity negative cosmological constant any dimension. Wormholes the Euclidean path integral gravity cause these states to have small, but non-zero, quantum mechanical overlaps that a universal form. The dramatic consequence: span Hilbert space log dimension equal Bekenstein-Hawking entropy. semiclassical we contain Einstein-Rosen bridges arbitrary size behind their horizons. Our...

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions terms collapsing dust shells the hole interior. Quantum mechanical wormholes cause these states to exponentially small, but universal, overlaps. show that overlaps imply span a Hilbert space log dimension equal event horizon area divided by four times Newton constant, explaining statistical origin Bekenstein-Hawking entropy.