Pseudo Complex General Relativity

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 super-massive 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 pseudo-complex (pc) coordinates, otherwise for weak gravitational fields non-physical ghost solutions appear. Thus, the need to use pc-variables. We will see, that the theory contains a minimal length, with important consequences. After that, the pc-GR 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 semi-classical Quantum Mechanics. The main point is that pc-GR 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 pc-GR will keep a remnant of the pc-description, 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 non-rotating massive object it is the pc-Schwarzschild solution, for a rotating massive object the pc-Kerr solution and for a charged massive object it will be the Reissner-Nordström solution. This chapter serves to become familiar on how to resolve problems in pc-GR 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 so-called galactic black holes are within pc-GR still there, but with the absence of an event horizon! Chapter 4 gives another application of the theory, namely the Robertson-Walker 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.

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

It has been over 100 years since the presentation of the Theory of General Relativity by Albert Einstein, in its final formulation, to the Royal Prussian Academy of Sciences. To celebrate 100 years of general relativity, World Scientific publishes this volume with a dual goal: to assess the current status of the field of general relativity in broad terms, and discuss future directions. The volume thus consists of broad overviews summarizing major developments over the past decades and their perspective contributions.

State-of-the-art survey by leading experts in the field. Major foci are superheavy nuclei and neutron-rich exotic nuclei. In addition new developments in nuclear fission and nuclear cluster decay are shown. Finally developments in relativistic heavy ion collisions and the physics of supercritical fields are detailed.

Walter Greiner (1935-2016) was a German physicist of the Goethe University, Frankfurt, well-known for his many contributions in scientific research and developments, in particular the field of nuclear physics. He was a well-respected science leader and a teacher who had supervised batches of young collaborators and students, many of whom are now leaders in both academics and industry worldwide. Greiner had a wide interest of science which covered atomic physics, heavy-ion physics, and nuclear astrophysics. Greiner co-founded GSI, the Helmholtz Centre for Heavy Ion Research, and the multi-disciplinary research center, FIAS (Frankfurt Institute for Advanced Studies). Besides numerous professorship with universities worldwide, including the University of Maryland, Greiner received many prestigious prizes in honor of his outstanding contributions, among others are the Otto Hahn Prize and the Max Born Prize. This memorial volume is a special tribute by Greiner's former colleagues, students, and friends honoring his contributions and passion in science. The volume begins with a writing by Greiner about his early days in science. The subsequent articles, comprising personal and scientific reminiscences of Walter Greiner, serve as timely reviews on various topics of current interest. Contents: Preface Reflections on My Youth and Early Years in Science (Walter Greiner) The Early Work of Walter Greiner (1960-1968) (Şerban Mişicu) Photon Scattering off Nuclei (Hartmuth Arenhövel) The QCD Phase Diagram from Statistical Model Analysis (Marcus Bleicher, Jan Steinheimer and Reinhard Stock) Why May Hydrodynamics Work for Classical Radiation Field? (Tamás S Biró) Chiral Symmetry Restoration and Deconfinement in Heavy-Ion Collisions (E L Bratkovskaya, W Cassing, P Moreau and A Palmese) The Physics Case for the √SNN ≈ 10 GeV Energy Region (J Cleymans) Untangling Simple Patterns in Intricate Atomic Nuclei (Jerry P Draayer, Kristina D Launey, Tomás Dytrych, Alison C Dreyfuss, Grigor H Sargsyan and Robert B Baker) Can One Determine the Neutrino Mass by Electron Capture? (Amand Faessler) Open and Hidden Charm in My Collaboration with Walter Greiner (Mark I Gorenstein) Dark Mater Compact Stars in Pseudo-Complex General Relativity (D Hadjimichef, G L Volkmer, R O Gomes and C A Zen Vasconcellos) Some Aspects of Nuclear Structure (J H Hamilton, A V Ramayya and E H Wang) The Power of the Geometrical Model of the Nucleus (Peter O Hess) Pseudo-Complex General Relativity: Theory (Peter O Hess and Thomas Boller) Observational Tests of the Pseudo-Complex Theory with Black Hole Imaging (Thomas Boller and Peter O Hess) From Strangeness Enhancement to Quark-Gluon Plasma Discovery (Peter Koch, Berndt Müller and Johann Rafelski) Time-Dependent Perturbation Theory as a Basis for Combined Many-Body-Perturbation and QED (Ingvar Lindgren) The Fullerene-Like Structure of Superheavy Element Z = 120 (Greinerium) -- A Tribute to Walter Greiner (Ş Mişicu and I N Mishustin) Cluster Radioactivity -- Past and Future (D N Poenaru and R A Gherghescu) Nuclear Mean-Field Models and Super-Heavy Elements (P-G Reinhard) The Octupole Collective Hamiltonian. Does It Follow the Example of the Quadrupole Case? (Stanislaw G Rohozinski and Leszek Próchniak) Modeling Hybrid Stars (S Schramm) Elliptic Flow and the Nuclear Equation of State (W Trautmann and H H Wolter) Black Holes and High Energy Physics: From Astrophysics to Lar

With contributions by leading theoreticians, this book presents the discoveries of hitherto hidden connections between seemingly unrelated fields of fundamental physics. The topics range from cosmology and astrophysics to nuclear-, particle- and heavy-ion science. A current example concerns the sensitivity of gravitational wave spectra to the phase structure of dense nuclear and quark matter in binary neutron star collisions. The contributions by Hanauske and Stoecker as well as Banik and Bandyopadhyay relate the consequent insights to hot dense nuclear matter created in supernova explosions and in high-energy heavy-ion collisions. Studies of the equation of state for neutron stars are also presented, as are those for nuclear matter in high-energy heavy-ion collisions. Other reviews focus on QCD-thermodynamics, charmed mesons in the quark-gluon plasma, nuclear theory, extensions to the standard general theory of relativity, new experimental developments in heavy ion collisions and renewable energy networks. The book will appeal to advanced students and researchers seeking a broad view of current challenges in theoretical physics and their interconnections.

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research papers, for pedagogical r- sons. Familiarity with fibre-bundle theory is certainly helpful, but in many cases I only rely on two-spinor calculus and conformally invariant concepts in gravitational physics. The key concepts the book is devoted to are complex manifolds, spinor techniques, conformal gravity, ?-planes, ?-surfaces, Penrose transform, complex 3 1 – – space-time models with non-vanishing torsion, spin- fields and spin- potentials. 2 2 Problems have been inserted at the end, to help the reader to check his und- standing of these topics. Thus, I can find at least four reasons for writing yet another book on spinor and twistor methods in general relativity: (i) to write a textbook useful to - ginning graduate students and research workers, where two-component spinor c- culus is the unifying mathematical language.

Recent discoveries in astronomy and relativistic astrophysics as well as experiments on particle and nuclear physics have blurred the traditional boundaries of physics. It is believed that at the birth of the Universe, a whirlwind of matter and antimatter, of quarks and exotic leptons, briefly appeared and merged into a sea of energy. The new phenomena and new states of matter in the Universe revealed the deep connection between quarks and the Cosmos. Motivated by these themes, this book discusses different topics: gravitational waves, dark matter, dark energy, exotic contents of compact stars, high-energy and gamma-ray astrophysics, heavy ion collisions and the formation of the quark-gluon plasma in the early Universe. The book presents some of the latest researches on these fascinating themes and is useful for experts and students in the field.