Titlebook: Einstein‘s General Theory of Relativity; With Modern Applicat Øyvind Grøn,Sigbjørn Hervik Textbook 2007 Springer-Verlag New York 2007 Cosmo

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https://doi.org/10.1007/978-3-662-28706-4In this chapter we will perform a 3+1 decomposition of the spacetime. This decomposition is very useful for various applications, in particular, we will use the 3+1 decomposition to derive a Lagrangian and Hamiltonian formalismof general relativity. We will also see howthe singularity theoremcan be described in this framework.

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Relativity Principles and GravitationTo obtain a mathematical description of physical phenomena, it is advantageous to introduce a reference frame in order to keep track of the position of events in space and time. The choice of reference frame has historically depended upon the view of human beings and their position in the Universe.

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Non-inertial Reference FramesIn this chapter we shall consider some consequences of the formalism developed so far, by studying the relativistic kinematics in two types of non-inertial reference frames: the rotating reference frame and the uniformly accelerating reference frame.

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Covariant Decomposition, Singularities, and Canonical CosmologyIn this chapter we will perform a 3+1 decomposition of the spacetime. This decomposition is very useful for various applications, in particular, we will use the 3+1 decomposition to derive a Lagrangian and Hamiltonian formalismof general relativity. We will also see howthe singularity theoremcan be described in this framework.

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https://doi.org/10.1007/978-3-8349-6454-0d 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.