  We embed spherical Rindler space -- a geometry with a spherical hole in its
center -- in asymptotically AdS spacetime and show that it carries a
gravitational entropy proportional to the area of the hole. Spherical
AdS-Rindler space is holographically dual to an ultraviolet sector of the
boundary field theory given by restriction to a strip of finite duration in
time. Because measurements have finite durations, local observers in the field
theory can only access information about bounded spatial regions. We propose a
notion of Residual Entropy that captures uncertainty about the state of a
system left by the collection of local, finite-time observables. For
two-dimensional conformal field theories we use holography and the strong
subadditivity of entanglement to propose a formula for Residual Entropy and
show that it precisely reproduces the areas of circular holes in AdS3.
Extending the notion to field theories on strips with variable durations in
time, we show more generally that Residual Entropy computes the areas of all
closed, inhomogenous curves on a spatial slice of AdS3. We discuss the
extension to higher dimensional field theories, the relation of Residual
Entropy to entanglement between scales, and some implications for the emergence
of space from the RG flow of entangled field theories.
