Flow-geometry microstates

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, $S_{\mathrm{dS}}=A_{\mathrm{horizon}}^{\mathrm{dS}}/4G$. 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.

59 pages, 22 figures; v2: published version, sections rearranged, introduction and discussion slightly expanded, references added