This book explores the role of singularities in general relativity (GR): The theory predicts that when a sufficient large mass collapses, no known force is able to stop it until all mass is concentrated at a point. The question arises, whether an acceptable physical theory should have a singularity, not even a coordinate singularity. The appearance of a singularity shows the limitations of the theory. In GR this limitation is the strong gravitational force acting near and at a supermassive concentration of a central mass. First, a historical overview is given, on former attempts to extend GR (which includes Einstein himself), all with distinct motivations. It will be shown that the only possible algebraic extension is to introduce pseudocomplex (pc) coordinates, otherwise for weak gravitational fields nonphysical ghost solutions appear. Thus, the need to use pcvariables. We will see, that the theory contains a minimal length, with important consequences. After that, the pcGR is formulated and compared to the former attempts. A new variational principle is introduced, which requires in the Einstein equations an additional contribution. Alternatively, the standard variational principle can be applied, but one has to introduce a constraint with the same former results. The additional contribution will be associated to vacuum fluctuation, whose dependence on the radial distance can be approximately obtained, using semiclassical Quantum Mechanics. The main point is that pcGR predicts that mass not only curves the space but also changes the vacuum structure of the space itself. In the following chapters, the minimal length will be set to zero, due to its smallness. Nevertheless, the pcGR will keep a remnant of the pcdescription, namely that the appearance of a term, which we may call "dark energy", is inevitable. The first application will be discussed in chapter 3, namely solutions of central mass distributions. For a nonrotating massive object it is the pcSchwarzschild solution, for a rotating massive object the pcKerr solution and for a charged massive object it will be the ReissnerNordstrom solution. This chapter serves to become familiar on how to resolve problems in pcGR and on how to interpret the results. One of the main consequences is, that we can eliminate the event horizon and thus there will be no black holes. The huge massive objects in the center of nearly any galaxy and the socalled galactic black holes are within pcGR still there, but with the absence of an event horizon! Chapter 4 gives another application of the theory, namely the RobertsonWalker solution, which we use to model different outcomes of the evolution of the universe. Finally the capability of this theory to predict new phenomena is illustrated.
About Peter O. Hess
Prof. Dr. Peter O. Hess, Mexico Dr. Mirko Schafer, Frankfurt, Germany Prof. Dr. Dr. h. c. mult. Walter Greiner, Frankfurt, GermanyDetails Book
Author  :  Peter O. Hess 
Publisher  :  Springer International Publishing AG 
Data Published  :  09 December 2015 
ISBN  :  3319250604 
EAN  :  9783319250601 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  257 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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