Exact vacuum solution to conformal Weyl gravity and galactic rotation curves
TL;DR: In this paper, the exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented, which includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance.
Abstract: The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.
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TL;DR: Various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds are reviewed.
Abstract: Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.
3,375 citations
Cites background from "Exact vacuum solution to conformal ..."
...At the end of this section we should mention conformal gravity in which the conformal invariance forces the gravitational action to be uniquely given by a Weyl action [414, 340]....
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TL;DR: Extended Theories of Gravity as discussed by the authors can be considered as a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales, which is an approach that, by preserving the undoubtedly positive results of Einstein's theory, is aimed to address conceptual and experimental problems recently emerged in astrophysics, cosmology and High Energy Physics.
2,776 citations
University of Lisbon1, University of Mississippi2, Institut d'Astrophysique de Paris3, Perimeter Institute for Theoretical Physics4, Sapienza University of Rome5, California Institute of Technology6, University of Cambridge7, Cornell University8, Max Planck Society9, Princeton University10, Montana State University11, University of Oxford12, McMaster University13, University of Aveiro14, University of Tübingen15, Naresuan University16, Rochester Institute of Technology17, University of Oldenburg18, Georgia Institute of Technology19, University of Illinois at Urbana–Champaign20, University of Wisconsin–Milwaukee21, University of Florida22, The Chinese University of Hong Kong23, Northwestern University24, Case Western Reserve University25, Sao Paulo State University26, Cardiff University27, Imperial College London28, Grand Valley State University29, Kyoto University30
TL;DR: In this article, a catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory is presented, and the current understanding of the structure and dynamics of compact objects in these theories is summarized.
Abstract: One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.
1,066 citations
TL;DR: In this paper, the authors discuss some cosmological and astrophysical applications where the issues related to the dark components are addressed by enlarging the Einstein theory to more general f (R) Lagrangians, where f(R) is a generic function of Ricci scalar R, not assumed simply linear.
Abstract: Astrophysical observations are pointing out huge amounts of “dark matter” and “dark energy” needed to explain the observed large scale structure and cosmic dynamics. The emerging picture is a spatially flat, homogeneous Universe undergoing the today observed accelerated phase. Despite of the good quality of astrophysical surveys, commonly addressed as Precision Cosmology, the nature and the nurture of dark energy and dark matter, which should constitute the bulk of cosmological matter-energy, are still unknown. Furthermore, up to now, no experimental evidence has been found, at fundamental level, to explain such mysterious components. The problem could be completely reversed considering dark matter and dark energy as “shortcomings” of General Relativity in its simplest formulation (a linear theory in the Ricci scalar R, minimally coupled to the standard perfect fluid matter) and claiming for the “correct” theory of gravity as that derived by matching the largest number of observational data, without imposing any theory a priori. As a working hypothesis, accelerating behavior of cosmic fluid, large scale structure, potential of galaxy clusters, rotation curves of spiral galaxies could be reproduced by means of extending the standard theory of General Relativity. In other words, gravity could acts in different ways at different scales and the above “shortcomings” could be due to incorrect extrapolations of the Einstein gravity, actually tested at short scales and low energy regimes. After a survey of what is intended for Extended Theories of Gravity in the so called “metric” and “Palatini” approaches, we discuss some cosmological and astrophysical applications where the issues related to the dark components are addressed by enlarging the Einstein theory to more general f (R) Lagrangians, where f (R) is a generic function of Ricci scalar R, not assumed simply linear. Obviously, this is not the final answer to the problem of “dark-components” but it can be considered as an operative scheme whose aim is to avoid the addition of unknown exotic ingredients to the cosmic pie.
907 citations
TL;DR: Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter as mentioned in this paper.
Abstract: ▪ Abstract Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below ao ≈ 10−8 cm/s2 ≈ cHo/6 the effective gravitational attraction approaches , where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V4 that forms the basis for the observed luminosity–rotation velocity relation—the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to superclusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extention of MOND to cosmology and structure formation.
821 citations
Cites methods from "Exact vacuum solution to conformal ..."
...He uses this argument to rule out the Mannheim & Kazanas (1989) spherical vacuum solution for Weyl conformal gravity in which φ(r) contains such a linear term....
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