Microcanonical Path Integrals and the Holography of small Black Hole Interiors

Abstract

We use a microcanonical path integral closely related to that introduced by Brown and York in 1992 to add new entries to the AdS/CFT dictionary concerning the interiors of small black holes. Stationary points of such path integrals are also stationary points of more standard canonical-type path integrals with fixed boundary metric, but the condition for dominance is now maximizing Hubeny-Rangamani-Takayanagi entropy at fixed energy. As a result, such path integrals can bring to the fore saddles that fail to dominate in more familiar contexts. We use this feature to argue that the standard Kruskal-like two-sided extension of small AdS black holes with energy $E_0$ is dual to a microcanonical version of the thermofield double state for AdS black holes that maximize the microcanonical bulk entropy at this energy. We also comment on entanglement in such states and on quantum effects that become large when the energy-width of the microcanonical ensemble is sufficiently small.

19 pages, 1 figure, typo fixed

References in corpus (9)

• Complexity and Shock Wave Geometries
• Setting the boundary free in AdS/CFT
• Deriving covariant holographic entanglement
• Holographic complexity is nonlocal
• From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
• A proposal of the gauge theory description of the small Schwarzschild black hole in AdS${}_5\times$S${}^5$
• Black-Hole Entropy from Supergravity Superstrata States
• Small AdS black holes from SYM
• Submatrix deconfinement and small black holes in AdS

Cited by in corpus (33)

• Flat entanglement spectra in fixed-area states of quantum gravity
• Eigenstate Thermalization and Disorder Averaging in Gravity
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• Partial Deconfinement
• Observing black holes through holographic superconductors
• Gravity Dual of Connes Cocycle Flow
• Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT
• Microcanonical Action and the Entropy of Hawking Radiation
• String Stars in Anti de Sitter Space
• Holographic Renyi Entropy at High Energy Density
• A precision test of averaging in AdS/CFT
• A Holographic Argument for the Penrose Inequality in AdS
• Holographic excited states in AdS Black Holes
• The Penrose Inequality as a Constraint on the Low Energy Limit of Quantum Gravity
• Stability of the microcanonical ensemble in Euclidean Quantum Gravity
• Restricted Maximin surfaces and HRT in generic black hole spacetimes
• The double cone geometry is stable to brane nucleation
• The Spacetime Geometry of Fixed-Area States in Gravitational Systems
• Wormholes from Averaging over States
• Black hole wavefunctions and microcanonical states
• Tunneling to Holographic Traversable Wormholes
• Constraining higher order gravities with subregion duality
• Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture
• An infinity of black holes
• Counting atypical black hole microstates from entanglement wedges
• A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)
• On Penrose inequality in holography
• Overdamped quasibound states inside a Schwarzschild black hole
• Energy spectrum of a quantum spacetime with boundary
• Gravitational thermodynamics without the conformal factor problem: Partition functions and Euclidean saddles from Lorentzian Path Integrals
• Complex Saddles of Charged-AdS Gravitational partition function
• Euclidean and complex geometries from real-time computations of gravitational Rényi entropies