Marginally outer trapped tubes in de Sitter spacetime

Area of Science:

• General Relativity
• Differential Geometry
• Mathematical Physics

Background:

• Marginally outer trapped surfaces (MOTSs) are crucial for defining black hole horizons.
• Constructing marginally outer trapped tubes (MOTTs) in de Sitter spacetime presents unique challenges.
• Previous work established existence of CMC surfaces in spheres, relevant for MOTT construction.

Purpose of the Study:

• To investigate the properties of MOTSs in de Sitter spacetime.
• To prove the existence of complete MOTTs with constant mean curvature (CMC) sections in de Sitter spacetime.
• To analyze the stability of MOTSs and their implications for MOTTs.

Main Methods:

• Analysis of spacetimes satisfying the null convergence condition and possessing a timelike conformal Killing vector.
• Application of a scaling argument to translate results from spherical geometry to de Sitter spacetime.
• Comparison with existing area laws for holographic screens.

Main Results:

• Demonstrated that all MOTSs in spacetimes with specific conditions are unstable.
• Proved the existence of complete MOTTs with CMC sections in de Sitter spacetime.
• Showed that the area of these CMC sections strictly increases monotonically.

Conclusions:

• The instability of MOTSs prevents standard propagation results from applying to MOTTs.
• The existence of complete MOTTs with CMC sections in de Sitter spacetime is established.
• The monotonic increase in CMC section area offers insights into holographic screen properties.