Schwarzschild de Sitter and extremal surfaces
arXiv:1910.11788 · doi:10.1140/epjc/s10052-020-08437-2
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.
Latex, 25pgs incl. appendices, 4 eps figs; v2: minor clarifications, references added; v3: minor corrections; v4: 30pgs, comments section added, matches version to be published