Energy- Momentum Relation in a Curved Space– Time Using General Relativity and Potential Dependent Special Relativity

Abstract

A new energy– momentum relation has been derived using the proper space – time expression in a curved space time. This relation link general and special relativity together. It describes how gravity affect particle energy. It also promotes the special relativity energy relation by recognizing the effect of fields through the potential term. This new expression reduces to the special relativistic one in a Minkoskian space. It also reduces to the Newtonian one for low speeds compared to the speed of light. This expression shows also that the energy is strongly affected by the space- time deformation through the time and space metrices. This new energy- momentum relation which link general with special relativity indicates that Einstein relativity theory is still one of the big achievements in physics