Titlebook: Einstein‘s General Theory of Relativity; With Modern Applicat ?yvind Gr?n,Sigbj?rn Hervik Textbook 2007 Springer-Verlag New York 2007 Cosmo

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Einstein’s Field Equationsd gravitational masses, was that there is no gravitational force at all. What is said to be “particle motion under the influence of the gravitational force” in Newtonian theory, is according to the general theory of relativity, free motion along geodesic curves in a curved space-time.

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Vectors, Tensors, and Formsformalism will be used to give a mathematical formulation of the fundamental principles of the general theory of relativity. It will also be employed to give an invariant formulation of Maxwell’s equations so that the equations can be applied with reference to an arbitrary basis in curved spacetime.

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Curvature It is easy to visualize curves and surfaces in three-dimensional space but it is difficult to grasp visually what curvature means in three-dimensional space, or worse still, in four-dimensional space-time. However the curvature of such spacesmay be discussed using the lower dimensional analogues of

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The Linear Field Approximationhe gravitational field moves slowly compared to the velocity of light. In the case of mass distributions of limited extension the field is weak at distances much larger than the Schwarzschild radius of the mass (see Chapter 10). At such distances the absolute value of the gravitational potential is

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The Schwarzschild Solution and Black Holesn to these equations. The solution is due to the astronomer Karl Schwarzschild, and in his honour the solution is referred to as the .. This solution represents a spacetime outside a non-rotating black hole. The Kerr solution representing spacetime outside a rotating black hole will also be deduced.

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Homogeneous and Isotropic Universe Modelsvitation, involves attraction between celestial bodies. However, very little is said of the evolution of the universe itself. The universe was believed to be static, and its evolution was beyond any physical theory. But after the year 1917, things were different. Within two years after the birth of