What drives the time evolution of the spacetime geometry?

Abstract

I show that in a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of degrees of freedom in the bulk and the boundary of a region. This expresses the gravitational field equation in the thermodynamic language which is the natural description, if gravity is an emergent phenomenon. In all static spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk; i.e., these spacetimes maintain holographic equipartition. It is the departure from holographic equipartition that drives the time evolution of the spacetime. This result, which is equivalent to Einstein's equations, provides an elegant, holographic, description of spacetime dynamics.Comment: Essay selected for the Third Award in the Gravity Research Foundation Essay Contest, 2014 (with minor editing); for more details, see arXiv:1312.325