Schwarzschild de Sitter and extremal surfaces

TL;DR

This paper investigates extremal surfaces in Schwarzschild de Sitter spacetime, revealing new timelike and spacelike surfaces with interesting horizon behaviors, including limits near the cosmological horizon and Nariai configurations.

Contribution

It identifies and characterizes novel extremal surfaces in Schwarzschild de Sitter space, including their limits and structures near horizons, extending previous work on such surfaces.

Findings

Timelike extremal surfaces connect future and past boundaries near horizons.

Spacelike extremal surfaces stretch indefinitely through the Penrose diagram.

Special structures emerge in de Sitter and Nariai limits.

Abstract

We study extremal surfaces in the Schwarzschild de Sitter spacetime with real mass parameter. We find codim-2 timelike extremal surfaces stretching between the future and past boundaries that pass through the vicinity of the cosmological horizon in a certain limit. These are analogous to the surfaces in arXiv:1711.01107 [hep-th]. We also find spacelike surfaces that never reach the future/past boundaries but stretch indefinitely through the extended Penrose diagram, passing through the vicinity of the cosmological and Schwarzschild horizons in a certain limit. Further, these exhibit interesting structure for de Sitter space (zero mass) as well as in the extremal, or Nariai, limit.