PHYSICAL REVIEW D 82, 064013 (2010) ‘‘Thermodynamics’’ of minimal surfaces and entropic origin of gravity
D. V. Fursaev
Dubna International University, Universiteskaya street 19, 141 980, Dubna, Moscow Region, Russia and Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia (Received 22 June 2010; published 8 September 2010) 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.
The fact that gravity is an emergent phenomenon dates back to ideas of the last century . A renewal of the interest to this point of view in the past years has been motivated by attempts to find a statistical explanation of the Bekenstein-Hawking entropy; see e.g. [2–4] and refer- ences therein. A possible source of the entropy are quantum correlations of underlying microscopical degrees of freedom across the black hole horizon [5–7].