The sufficiently trapped surface

TL;DR

The paper introduces the concept of sufficiently trapped surfaces, extending Penrose's trapped surfaces to quantum contexts, preserving their role in singularity theorems and cosmic censorship.

Contribution

It generalizes trapped surfaces to weaker energy conditions, maintaining their significance in singularity and area theorems under quantum effects.

Findings

Sufficiently trapped surfaces uphold key theorems despite null convergence violations.

They support the weak cosmic censorship conjecture in semiclassical gravity.

The concept bridges classical and quantum gravitational frameworks.

Abstract

Roger Penrose introduced the concept of the trapped surface: a spacelike hypersurface where the two null normals have negative expansion. The trapped surface along with the null convergence condition leads to null geodesic incompleteness. If an event horizon forms, the trapped surface is also always behind it, providing evidence for the weak cosmic censorship conjecture. When the null convergence condition is violated, as in the case of semiclassical gravity, trapped surfaces lose these guarantees. A generalized notion, the sufficiently trapped surface, accommodates weaker energy conditions consistent with quantum fields. This concept restores key roles in singularity and area theorems and continues to support the weak cosmic censorship conjecture.