Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging

TL;DR

This paper explores how averaging over internal dimensions and timelike boundaries in string/M theory can reconcile dS holography with black hole microstates, providing new insights into quantum gravity and horizon entropy.

Contribution

It demonstrates the role of internal averaging and timelike boundaries in connecting AdS and dS solutions within string/M theory, advancing the understanding of horizon microstates.

Findings

Microstate count matches Gibbons-Hawking entropy for dS3.

Boundary deformation relates black hole horizon to dS cosmic horizon.

Internal averaging washes out differences in extra dimensions.

Abstract

In this note, we resolve an apparent obstacle to string/M theory realizations of dS observer patch holography, finding a new role for averaging in quantum gravity. The solvable $T\bar T(+\Lambda_2)$ deformation recently provided a detailed microstate count of the $dS_3$ cosmic horizon, reproducing the refined Gibbons-Hawking entropy computed by Anninos et al along with the correct radial bulk geometry. On the gravity side, the deformation brings in the boundary to just outside a black hole horizon, where it is indistinguishable from the dS cosmic horizon, enabling a continuous passage to a bounded patch of dS. In string/M theory, the relationship between AdS/CFT and dS involves uplifts that change the internal topology, e.g. replacing an internal sphere $\mathbb{S}$ with an internal hyperbolic space $\mathbb{H}$ (and incorporating varying warp and conformal factors). We connect these two approaches, noting that the differences in the extra dimensions between AdS black hole and dS solutions are washed out by internal averaging in the presence of a timelike boundary skirting the horizon. This helps to motivate a detailed investigation into the possibility of such timelike boundaries in (A)dS solutions of string/M theory, and we take initial steps toward suitable generalizations of Liouville walls as one approach.