General Relativity is an extremely successful theory, at least for weak gravitational fields; however, it breaks down at very high energies, such as in correspondence to the initial singularity. ...Quantum Gravity is expected to provide more physical insights in relation to this open question. Indeed, one alternative scenario to the Big Bang, that manages to completely avoid the singularity, is offered by Loop Quantum Cosmology (LQC), which predicts that the Universe undergoes a collapse to an expansion through a bounce. In this work, we use metric f(R) gravity to reproduce the modified Friedmann equations which have been obtained in the context of modified loop quantum cosmologies. To achieve this, we apply an order reduction method to the f(R) field equations, and obtain covariant effective actions that lead to a bounce, for specific models of modified LQC, considering a massless scalar field.
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We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is ...non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of ...gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.
This open access monograph offers a detailed study and a systematic defense of a key intuition we typically have, as human beings, with respect to the nature of time: the intuition that the future is ...open, whereas the past is fixed. For example, whereas it seems unsettled whether there will be a fourth world war, it is settled that there was a first world war. The book contributes, in particular, three major and original insights. First, it provides a coherent, non-metaphorical, and metaphysically illuminating elucidation of the intuition. Second, it determines which model of the temporal structure of the world is most appropriate to accommodate the intuition, and settles on a specific version of the Growing Block Theory of time (GBT). Third, it puts forward a naturalistic foundation for GBT, by exploiting recent results of our best physics (viz. General Relativity, Quantum Mechanics, and Quantum Gravity). Three main challenges are addressed: the dismissal of temporal asymmetries as non-fundamental phenomena only (e.g., thermodynamic or causal phenomena), the epistemic objection against GBT, and the apparent tension between GBT and relativistic physics. It is argued that the asymmetry between the open future and the fixed past must be grounded in the temporal structure of the world, and that this is neither precluded by our epistemic device, nor by the latest approaches to Quantum Gravity (e.g., the Causal Set Theory). Aiming at reconciling time as we find it in ordinary experience and time as physics describes it, this innovative book will raise the interest of both academic researchers and graduate students working on the philosophy of time. More generally, it presents contents of interest for all metaphysicians and non-dogmatic philosophers of physics. This is an open access book.
The conceptual changes brought by modern physics are important, radical and fascinating, yet they are only vaguely understood by people working outside the field. Exploring the four pillars of modern ...physics – relativity, quantum mechanics, elementary particles and cosmology – this clear and lively account will interest anyone who has wondered what Einstein, Bohr, Schrödinger and Heisenberg were really talking about. The book discusses quarks and leptons, antiparticles and Feynman diagrams, curved space-time, the Big Bang and the expanding Universe. Suitable for undergraduate students in non-science as well as science subjects, it uses problems and worked examples to help readers develop an understanding of what recent advances in physics actually mean.
There are some gravitational theories in which the ordinary energy–momentum conservation law is not valid in the curved space–time. Rastall gravity is one of the known theories in this regard, which ...includes a non-minimal coupling between geometry and matter fields. Equipped with the basis of such theory, we study the properties of traversable wormholes with flat asymptotes. We investigate the possibility of exact solutions by a source with the baryonic matter state parameter. Our survey indicates that Rastall theory has considerable effects on the wormhole characteristics. In addition, we study various case studies and show that the weak energy condition may be met for some solutions. We also give a discussion regarding traversibility of such wormhole geometry with phantom sources.
The differential cross-section for the inclusive production of ψ(2S) mesons in pp collisions at s√=7 TeVs=7 TeV has been measured with the LHCb detector. The data sample corresponds to an integrated ...luminosity of 36 pb−1. The ψ(2S) mesons are reconstructed in the decay channels ψ(2S)→μ + μ − and ψ(2S)→J/ψπ + π −, with the J/ψ meson decaying into two muons. Results are presented both for promptly produced ψ(2S) mesons and for those originating from b-hadron decays. In the kinematic range p T(ψ(2S))≤16 GeV/c and 2<y(ψ(2S))≤4.5 we measure
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where the last uncertainty on the prompt cross-section is due to the unknown ψ(2S) polarization. Recent QCD calculations are found to be in good agreement with our measurements. Combining the present result with the LHCb J/ψ measurements we determine the inclusive branching fraction
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where the last uncertainty is due to the (b→J/ψX)B(b→J/ψX) , (J/ψ→μ+μ−)B(J/ψ→μ+μ−) and (ψ(2S)→e+e−)B(ψ(2S)→e+e−) branching fraction uncertainties.
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