Abstract
Deformations of minimal surfaces lying in constant-time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby pointlike particles is found. It allows one to introduce a local temperature on the surface and represent variations of its area in a thermodynamical form by assuming that the entropy in the Planck units equals the quarter of the area. These results provide a strong support to a recent hypothesis that gravity has an entropic origin, the minimal surfaces being a sort of holographic screens. The gravitational entropy also acquires a definite physical meaning related to quantum entanglement of fundamental degrees of freedom across the screen.
- Received 22 June 2010
DOI:https://doi.org/10.1103/PhysRevD.82.064013
© 2010 The American Physical Society