Field Approach for General Relativity

The general theory of relativity is based on expressing gravity by means of the metric tensor and its elements instead of some fields as in electrodynamics. This work starts with by defining some vector fields for metric or metric tensor. After metric and metric tensor are expressed in terms of these fields, the geodesic equations and Einstein equations are derived for these fields. Finally, perihelion precession and light deflection are recalculated, as two different applications of the introduced fields.

On the Nature of Exotic Matter in Morris-Thorne Wormholes

It is well known that phantom energy, which is characterized by the equation of state p = ωρ, ω < −1, can support Morris-Thorne wormholes since it leads to a violation of the null energy condition. The purpose of this note is to show that the converse is also true in the following sense: for a typical shape function, the equation of state of exotic matter in the vicinity of the throat is given by p↓r = ωρ, ω < −1, where pr is the radial pressure.