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 [1]. 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].*

Change that to our future event horizon.