Energy condition

In the general theory of relativity, mass and energy distribution is described with an energy -momentum tensor. Energy conditions are inequalities for contraction of this tensor in the framework of this theory. Apply this energy conditions in the Singularitätentheoremen, of which several versions exist and differ in the strength of the applied energy condition. A strong condition results in easy to be proved causal singularities, but there may be forms of matter in the universe which contradict this and obey only weaker energy conditions.

The weakest energy conditions ( light -like ) are very likely to be met by all matters, however, the situation will only follow light -like singularities.

The strong energy condition

The strong energy condition states that the energy -momentum tensor causes only attractive gravity, and is therefore a very clear condition that corresponds to the intuitive observation. In the formulation of the ART space curvatures describe the gravitational effects and are mathematically represented by the Ricci tensor. The strong energy condition now states that the double contraction of the energy-momentum tensor must be greater than 0 with an arbitrary time-like vector field. Such a vector field corresponding for example to the tangent vector to the world line of an observer and is thus the time axis of its local Lorentz system.

Via the Einstein field equations, this condition also translate as required for the energy -momentum tensor, by forming the trace inverse.

With the Krümmungsskalar, the trace of the energy-momentum tensor and a geometric and gravitational constant.

The weak energy condition

The weak energy condition also has an intuitive correspondence and demands that all observers, ie systems with time-like world lines, a positive energy density of the observed energy distribution see.

Energy condition for light -like vectors

This condition is often called zero - energy condition, as it relates to light -like vectors, which are also called zero vectors, since their dot product is zero by definition. This condition is substantially weaker than the previous two and is comprised of two as a special case in the limit of high speed.