A study of gravitational field equation in general relativity
Abstract
General relativity theory is considered an essential tool in terms of studying astronomical phenomenons such as black holes and universal expansion from theoretical perspective that is based on the mathematical derivations, and general relativity in its core is one of the most beautiful and revolutionary conceptions of modern science, that gravitational field is the geometry of four-dimensional curved space that we call spacetime, and the geometry of curvatures is the mathematical basis for general relativity, and gravitational field equation that is relativistically generalized is the main equation of this theory and we can use this equation for studying different gravitational fields like a gravitational field surrounds a black hole, so we have briefly derived this equation starting with traditional mechanics equations depending essentially on the mathematical basis in curves geometry, and depending on the geodesic equation of a particle moving inside a gravitational field, hence, reaching the most important results of general relativity theory such as black holes and gravitational waves.
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