Catálogo de publicaciones - libros

One of the most successful and useful applications of Einstein’s General Theory of Relativity is within the field of cosmology. Newton’s theory of gravitation, 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 the General Theory of Relativity, Einstein realized that this theory actually could say something about the universe and constructed a static universemodel as a solution of the relativistic field equations. The era of modern cosmology had begun, which would revolutionize our view of the universe.

Soon after Einstein had introduced the cosmological constant he withdrew it and called it “the biggest blunder” of his life. However, there has been developments in the last decades that have given new life to the cosmological constant. Firstly, the idea of gave cosmology a whole new view upon the first split second of our universe. A key ingredient in the inflationary model is the behaviour of models that have a cosmological constant-like behaviour. Secondly, recent observations may indicate that we live in an accelerated universe. The inclusion of a cosmological constant can give rise to such behaviour as we will show in this chapter. We will first start with the static solution that Einstein found and was the reason that Einstein introduced the cosmological constant in the first place.

In this chapter we will investigate anisotropic and inhomogeneous universe models. If we relax the cosmological principles a bit we can get new and interesting models of our universe. Actually, one of the main goals of cosmology today is to the isotropy and homogeneity the universe has and in order to explain a certain property of the universe one has to consider sufficiently generalmodels that need not have this property. In this chapter we will investigate the Bianchi type I universe model and the inhomogeneous Lemaître-Tolman-Bondi (LTB) universe models. The Bianchi type I model is the simplest of the spatially homogeneous models which allows for anisotropy and the LTB-models are inhomogeneous universe models with spherically symmetric three-space.

In 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.

In this section we will explore the concept of symmetries even further. We introduced some of the basics in chapter 6, and we will pursue the ideas further here. In doing so, we will generalise the FRW models to the Bianchi models which are in general spatially homogeneous but not necessarily isotropic.

A question that often arises in gravitational theory is what happens to the geometry of spacewhen there is a jump discontinuity in the energy-momentum tensor along a surface. For example, what is the connection between the curvature properties for the interior Schwarzschild solution and the exterior Schwarzschild solution? Here, along the boundary of some surface, the energy density experiences a jump discontinuity. Another analogous scenario is for example a shock wave propagating outwards from an exploding star. In models of such shock waves the density can be infinite.

In 1999, Lisa Randall and Raman Sundrumpresented a five-dimensional model for our universe [RS99b, RS99a]. They imagined our four-dimensional world as a or a surface layer in a five-dimensional bulk. This bulk may be infinite in size, but due to the special properties of the bulk the gravitational fields are effectively localised to the brane. The other standard model fields are confined to the brane; only gravity is allowed to propagate in the fifth dimension.

Already in 1914 – before Einstein had fulfilled the construction of the general theory of relativity – Gunnar Nordström1 had published a five-dimensional scalar-tensor theory of gravitation in an effort to unify gravitation and electromagnetism. Since it was based upon his own theory of gravitation which was soon surpassed by Einstein’s theory, this work was neglected for several decades.