de Sitter space, extremal surfaces and "time-entanglement"

Understand

We refine previous investigations on de Sitter space and extremal surfaces anchored at the future boundary $I^+$.

• Since such surfaces do not return, they require extra data or boundary conditions in the past (interior).
• In entirely Lorentzian de Sitter spacetime, this leads to future-past timelike surfaces stretching between $I^\pm$.
• Apart from an overall $-i$ factor (relative to spacelike surfaces in $AdS$) their areas are real and positive.