Black Holes Hint Towards De Sitter-Matrix Theory

TL;DR

The paper argues that de Sitter holography is best described by a matrix quantum mechanics (dS-matrix) for the static patch, with horizon degrees of freedom organized into block-diagonal matrix sectors that encode a small black hole and the surrounding cosmic horizon. It shows that both small and large black-hole regimes yield entropy-deficit–driven fluctuations whose rates match between gravitational calculations and matrix-model expectations, with the Nariai geometry acting as a universal saddle that governs inside-out horizon exchange. A dynamical mechanism, via constrained off-diagonal matrix elements and an additional radial matrix, is proposed to enforce the constraints and reproduce the correct deficit scaling, modulo tunable numerical factors. The work draws deep connections between instanton-like nonperturbative transitions in large-N theories and Boltzmann fluctuations in de Sitter space, suggesting a unified, matrix-based holographic description with broad implications for the holographic principle in spacetimes with a positive cosmological constant.

Abstract

De Sitter black holes and other non-perturbative configurations can be used to probe the holographic degrees of freedom of de Sitter space. For small black holes evidence was first given in seminal work of Banks, Fiol, and Morrise; and followups by Banks and Fischler; showing that dS is described by a form of matrix theory. For large black holes the evidence given here is new: Gravitational calculations and matrix theory calculations of the rates of exponentially rare fluctuations match one another in surprising detail. The occurrence of the Nariai geometry and the "inside-out" transition are especially interesting examples which I explain.

Figures (11)

• Figure 1: The left panel shows the Penrose diagram for de Sitter space with a particular choice of opposing static patches. The blue and pink regions are the stretched horizons of the two SPs. The right panel shows the spatial geometry of a time-symmetric slice. The blue and pink surfaces represent the stretched horizons.
• Figure 2: A $t=0$ slice of dS and the stretched horizons shown as light blue and pink great circles. The dark blue surface is homologous to the light blue horizon. It can be shrunk to a point.
• Figure 3: The dark blue curve represents the minimal surface lying between the two stretched horizons shown in light blue and pink.
• Figure 4: In both panels the black dots represent the anchoring points of a space-like surface $\Sigma$ connecting the two horizons at a particular time. The minimal two-sphere cutting $\Sigma$ lies at the anchoring points.
• Figure 5: The function $g(r)$ and its zeros, $r_0$ and $r_{\pm}.$