Flow-geometry microstates

TL;DR

This paper constructs and counts geometric microstates for two-dimensional flow geometries that interpolate between AdS and dS spacetimes, reproducing the Gibbons-Hawking entropy and providing a holographic realization of de Sitter microstates.

Contribution

It introduces a method to construct and count dS microstates via flow geometries with particles behind the horizon, extending microstate counting to finite-length Einstein-Rosen bridges.

Findings

Microstates reproduce Gibbons-Hawking entropy.

Infinite-length ER bridge microstates constructed.

Finite-length ER bridge microstates also analyzed.

Abstract

We construct geometric microstates for a class of two-dimensional flow geometries$-$spacetimes that interpolate from an asymptotic AdS$_2$ boundary to a dS$_2$ static patch in the interior$-$by inserting particles behind the horizon. We show that this mechanism produces dS microstates with an Einstein-Rosen bridge of infinite length behind the horizon. The state-counting of these microstates, including wormhole contributions, reproduces the Gibbons-Hawking entropy, $S_{\rm dS}=A^{\rm dS}_{\rm horizon}/4G$. Furthermore, we extend the microstate-counting method to the case of a finite-length Einstein-Rosen bridge. As a result, the Hilbert space of the dS horizon in the flow geometry can be spanned by states with a purely dS Einstein-Rosen bridge, containing no AdS portion on the time-symmetric slice. This provides a concrete realization of dS microstates within a controlled holographic framework.