Twistors and Holography

TL;DR

This paper generalizes Bousso's lightsheet concept to 'timesheets' using twistor theory, linking entropy bounds to geometric and topological properties in twistor space, potentially simplifying holographic descriptions.

Contribution

It introduces 'timesheets' as deformations of lightsheets and connects entropy flux to twistor space volume, offering a novel geometric and topological framework for holography.

Findings

Timesheets are sections of twistor bundles over spacelike surfaces.

Increasing entropy flux relates to larger regions in twistor space.

Potential topological characterization of lightsheets in simple spacetimes.

Abstract

We extend Bousso's notion of a lightsheet - a surface where entropy can be defined in a way so that the entropy bound is satisfied - to more general surfaces. Intuitively these surfaces may be regarded as deformations of the Bousso choice; in general, these deformations will be timelike and so we refer to them as `timesheets'. We show that a timesheet corresponds to a section of a certain twistor bundle over a given spacelike two-surface B. We further argue that increasing the entropy flux through a given region corresponds to increasing the volume of certain regions in twistor space. We further argue that in twistor space, it might be possible to give a purely topological characterization of a lightsheet, at least for suitably simple spacetimes.