Einstein Field Equations - Vacuum Field Equations

Vacuum Field Equations

If the energy-momentum tensor is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting in the trace-reversed field equations, the vacuum equations can be written as

In the case of nonzero cosmological constant, the equations are

The solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.

Manifolds with a vanishing Ricci tensor, are referred to as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.

Read more about this topic:  Einstein Field Equations

Famous quotes containing the words vacuum and/or field:

    Teenagers who are never required to vacuum are living in one.
    Fred G. Gosman (20th century)

    When it had long since outgrown his purely medical implications and become a world movement which penetrated into every field of science and every domain of the intellect: literature, the history of art, religion and prehistory; mythology, folklore, pedagogy, and what not.
    Thomas Mann (1875–1955)