Title Extensions of f(R) gravity : curvature-matter couplings and hybrid metric-Palatini gravity / Tiberiu Harko (University College London), Francisco S.N. Lobo (Universidade de Lisboa)

Published Cambridge : Cambridge University Press, 2019

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Description 1 online resource Series Cambridge monographs on mathematical physics Cambridge monographs on mathematical physics. Contents Cover; Half-title; Series information; Title page; Copyright information; Contents; Preface; Acknowledgments; Part I Review of General Relativity; 1 Introduction; 2 The Mathematical Foundations; 2.1 Basic Mathematical Objects of Physics: Vectors and Tensors; 2.1.1 Scalars and Vectors; 2.1.2 Tensors; 2.1.3 Tensor Algebra; 2.2 Essentials of Riemannian Geometry; 2.2.1 The Metric Tensor; 2.2.2 The Equations of Motion and Geodesic Lines; 2.2.3 The Covariant Derivative; 2.3 The Riemann Curvature Tensor and Its Properties; 2.4 Summary; 3 The Gravitational Field Equations 3.1 The Variational Principle and the Field Equations3.1.1 The Variation of the Gravitational Action; 3.1.2 The Variation of the Matter Action; 3.1.3 The Einstein Gravitational Field Equations; 3.1.4 Particle Motion and the Newtonian Limit; 3.2 The Spherically Symmetric Gravitational Field; 3.2.1 The Metric for a Static and Spherically Symmetric Field; 3.2.2 The Gravitational Field Equations in Spherical Symmetry; 3.2.3 The Schwarzschild Solution; 3.3 Summary and Conclusions; 4 The Solar System Tests and Astrophysical Applications; 4.1 Classical Tests of General Relativity 4.1.1 The Perihelion Precession of Planetary Orbits4.1.2 The Deflection of Light; 4.1.3 The Shapiro Radar Echo Delay Test; 4.2 The Tolman-Oppenheimer-Volkoff Equation; 4.2.1 Constant Density General Relativistic Stars; 4.2.2 Exact Power Series Solutions of the Relativistic Structure Equations for a Linear Barotropic Fluid; 4.2.3 The Buchdahl Limit in the Presence of a Cosmological Constant; 4.3 Spherical Gravitational Collapse of Strange Quark Null Fluids; 4.3.1 Metric and Gravitational Field Equations; 4.3.2 The General Solution of the Field Equations 4.3.3 The Energy Conditions and the Singularity Properties4.3.4 The Formation of a Naked Singularity; 4.4 Steady Spherical Accretion in Arbitrary Spherically-Symmetric Space-times; 4.4.1 The Conservation Equations; 4.4.2 Accreting Fluids Satisfying a Polytropic Equation of State; 4.5 Electromagnetic Emission Properties of Thin Accretion Disks; 4.5.1 The Motion of Massive Particles in Stationary and Axially Symmetric Space-times; 4.5.2 Electromagnetic Emissivity Properties of Thin Accretion Disks; 4.6 Summary and Discussion; 5 Cosmology; 5.1 Newtonian Cosmology 5.1.1 The Energy Conservation Approach5.1.2 The Hydrodynamic Model; 5.1.3 The Neo-Newtonian Approach; 5.1.4 Gravitational Condensation of Dark Energy; 5.2 Relativistic Cosmology; 5.2.1 The Friedmann-Lemaître-Robertson-Walker Metric; 5.2.2 The Friedmann Equations; 5.2.3 Cosmological Constant, Vacuum Energy, or Dark Energy?; 5.2.4 Scalar Field Cosmologies with Arbitrary Self-Interaction Potential; 5.2.5 The Dark Matter Problem; 5.3 Open Questions and Going Beyond General Relativity; 6 f(R) Gravity; 6.1 Introduction; 6.2 The Gravitational Field Equations Summary Recent cosmological observations have posed a challenge for traditional theories of gravity: what is the force driving the accelerated expansion of the universe? What if dark energy or dark matter do not exist and what we observe is a modification of the gravitational interaction that dominates the universe at large scales? Various extensions to Einstein's General Theory of Relativity have been proposed, and this book presents a detailed theoretical and phenomenological analysis of several leading, modified theories of gravity. Theories with generalised curvature-matter couplings are first explored, followed by hybrid metric-Palatini gravity. This timely book first discusses key motivations behind the development of these modified gravitational theories, before presenting a detailed overview of their subsequent development, mathematical structure, and cosmological and astrophysical implications. Covering recent developments and with an emphasis on astrophysical and cosmological applications, this is the perfect text for graduate students and researchers Bibliography Includes bibliographical references and index Notes Print version record Subject Expanding universe. Curvature cosmology. Large scale structure (Astronomy) Gravitation. Cosmology. Gravitation cosmology. SCIENCE -- Astronomy. Cosmology Curvature cosmology Expanding universe Gravitation Large scale structure (Astronomy) Form Electronic book Author Lobo, Francisco S. N., author. ISBN 9781108645683 1108645682 9781108584579 1108584578

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