Black Hole Microstate Cosmology

TL;DR

<3-5 sentence high-level summary>: The paper investigates how certain high-energy holographic CFT states corresponding to black hole microstates encode geometry behind the horizon, modeled by an end-of-the-world brane with FRW worldvolume. It develops a BCFT/AdS construction and uses entanglement entropy of large boundary subsystems as a direct probe of behind-the-horizon physics, complemented by SYK-chain simulations and holographic complexity analyses. The results show that behind-horizon regions can influence boundary entanglement in a controlled time window, with SYK data qualitatively supporting the holographic picture, and reveal key distinctions between volume and action complexity in capturing this physics. A central take-home message is that a microscopic CFT description could, in principle, provide a complete account of cosmological-like dynamics on the ETW brane, though simple models struggle to realize a fully localized four-dimensional cosmology, hinting at richer bulk-bdyne coupled dynamics needed for realistic scenarios.

Abstract

In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations. A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.

Figures (31)

• Figure 1: Penrose diagram for spacetimes associated with certain black hole microstates. The spacetime terminates on the left with an effective end-of-the-world brane (shown in red on the left) whose worldvolume geometry is a four-dimensional FRW big bang/big crunch cosmology. For certain brane trajectories, the physics of the left region would correspond to a Randall-Sundrum II cosmology, with gravity localized on the brane. If there are CFT states that realize this scenario, the CFT would provide a complete microscopic description of this cosmology.
• Figure 2: Two possibilities for extremal surfaces and associated entanglement wedges (shaded) for ball-shaped boundary regions. The extremal surface on the right has the topology of $S^{d-2}$ times an interval, so is connected for $d > 2$.
• Figure 3: Time-dependence of subsystem entanglement entropy for a five-dimensional black hole microstate modeled by a constant tension ETW brane behind the horizon. Curves from bottom to top correspond to successively larger ball-shaped subsystems on the sphere. For large enough subsystems, the minimal area extremal surfaces probe behind the horizon for an interval of time.
• Figure 4: Path integral description of black hole microstates $|\Psi^\beta_{B} \rangle$.
• Figure 5: (a) The AdS/CFT correspondence, with an asymptotically AdS bulk $M_\text{AdS}$ and an asymptotic boundary $N_\text{CFT} = \partial M_\text{AdS}$. (b) The AdS/BCFT correspondence. We add a boundary to the CFT, whose holographic "image" is the ETW brane $Q$.