# On extremal surfaces and de Sitter entropy

Source: [On extremal surfaces and de Sitter entropy](<https://www.sota2.com/research/paper/68fa37f71e209131ce8b6ada>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T22:42:23.003Z

Authors: K. Narayan

Published: 2017-11-03T11:15:03.000Z

## Abstract

We study extremal surfaces in the static patch coordinatization of de Sitter space, focussing on the future and past universes. We find connected timelike codim-2 surfaces on a boundary Euclidean time slice stretching from the future boundary $I^+$ to the past boundary $I^-$. In a limit, these surfaces pass through the bifurcation region and have minimal area with a divergent piece alone, whose coefficient is de Sitter entropy in 4-dimensions. These are reminiscent of rotated versions of certain surfaces in the $AdS$ black hole. We close with some speculations on a possible $dS/CFT$ interpretation of 4-dim de Sitter space as dual to two copies of ghost-CFTs in an entangled state. For a simple toy model of two copies of ghost-spin chains, we argue that similar entangled states always have positive norm and positive entanglement.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1711.01107>)

[PDF](<https://arxiv.org/pdf/1711.01107.pdf>)