Maximal vacuum entanglement principle

I will discuss evidence supporting the hypothesis that entanglement entropy in small geodesic balls is maximal at fixed volume [1]. This is in a sense a microscopic version of the holographic principle, and the evidence for its validity hinges on the Einstein equation. I will also discuss the effort to derive the Einstein equation by assuming the hypothesis is valid, and some relevant results about entanglement variation [2,3,4].\\ \vskip 2mm \noindent [1] Ted Jacobson, arXiv/1505.04753\ [2] Horacio Casini, Damian A. Galante, Robert C. Myers, arXiv/1601.00528\ [3] Antony Speranza, in preparation\ [4] Madhavan Varadarajan, in preparation\