Abstract
We extend Bousso's notion of a lightsheet, a surface where entropy can be defined in a way such 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 2-surface B. We further argue that increasing the entropy flux through a given region of spacetime corresponds to increasing the volume of certain regions in twistor space. Put another way, it would seem that entropy in spacetime corresponds to volume in twistor space. We argue that this formulation may point a way towards a version of the covariant entropy bound which allows for quantum fluctuations of the lightsheet. We also point out that in twistor space, it might be possible to give a purely topological characterization of a lightsheet, at least for suitably simple spacetimes.
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