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2016

What is General Relativity?

Coley, Alan A., Wiltshire, David L.

Understand

General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of particles on the background.

But open questions remain, including: What is the scale on which matter and geometry are dynamically coupled in the Einstein equations? Are the field equations valid on small and large scales? What is the largest scale on which matter can be coarse grained while following a geodesic of a solution to Einstein's equations? We address these questions.
If the field equations are causal evolution equations, whose average on cosmological scales is not an exact solution of the Einstein equations, then some simplifying physical principle is required to explain the statistical homogeneity of the late epoch Universe.
Such a principle may have its origin in the dynamical coupling between matter and geometry at the quantum level in the early Universe.