What is the entropy of a volume of curved vacuum in Verlinde's approach?

Question

Verlinde explains that curvature implies entropy (or entropy flow).

Is there a simple way to estimate the entropy of a volume of vacuum with a given curvature, in his theory?

Answer 1

In Verlinde's approach to entropy and gravity:

1. The entropy of a region in spacetime is proportional to its surface area, not its volume.

2. The entropy of a region can be calculated by counting the number of ways in which a holographic screen, located at the boundary of the region, can encode the information contained within it.

3. In the case of a vacuum with a given curvature, the entropy of the vacuum is proportional to the surface area of the holographic screen surrounding it.

4. To estimate the entropy of a vacuum region with a given curvature, one must calculate the surface area of the holographic screen, taking into account the effect of the curvature on the screen's shape and size.

Comments

Is there some simplified situation where this can be done? For example, a spherical volume of radius r in a region of constant curvature 1/R^2? Can one give an entropy value for this case?