Einstein Equations

The quantitative description of the Universe by general relativity requires obtaining solutions to what are termed the Einstein field equations. These are ten equations that must be solved simultaneously; they are notoriously difficult, and only a few exact solutions are known.

Classes of Solutions

Among these solutions, there are two general classes. Static universes have distance scales that are constant in time, and dynamic universes are either expanding or contracting over time.

Static Solutions Are Unstable

Although it is beyond the scope of our introductory discussion to do so, it may be shown that the cosmological principle (the assumption that there are no preferred positions or directions in the Universe) is inconsistent with a static universe. That is, the cosmological principle requires that the Universe be either expanding or contracting, or unstably balanced between the two.