Informal Pizza Seminar

The Boundary as Distant Stars:
Mach's Principle in General Relativity

Justin Khoury

Perimeter Institute

General Relativity (GR) falls short of realizing the Machian idea of unique gravitational field for given matter distribution. This is because Einstein's equations must be supplemented with boundary/initial conditions. Here we show, however, that such boundary conditions can be interpreted as suitable (holographic) stress-energy pasted on the boundary — the distant stars. Thus GR is perfectly consistent with Mach's Principle provided one specifies both bulk and boundary matter. As a bonus, two other Machian properties are shown to be realized: 1. Absence of non-zero global charges, e.g. mass or angular momentum; 2. Total relativity of motion: arbitrary observers in the bulk can be made inertial by tweaking the matter on the boundary.