Spherically Symmetrical Models in General Relativity
01 Dec 1947-Monthly Notices of the Royal Astronomical Society (Oxford University Press)-Vol. 107, pp 410-425
TL;DR: In this paper, the field equations of general relativity are applied to pressure-free spherically symmetrical systemsof particles and the equations of motion are determined without the use of approximations and are compared with the Newtonian equations.
Abstract: The field equations of general relativity areapplied to pressure-free spherically symmetrical systemsof particles. The equations of motion are determinedwithout the use of approximations and are compared with the Newtonian equations. The total energyis found to be an important parameter, determining thegeometry of 3-space and the ratio of effectivegravitating to invariant mass. The Doppler shift isdiscussed and is found to contain both the velocity shiftand the Einstein shift combined in a rather complexexpression.
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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.
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TL;DR: In this article, an orthonormal tetrad system and associated coordinate system is obtained, which may be used to locally describe any dust-filled space-time, and three classes of solution with σ = 0, ω ≠ 0 are studied.
Abstract: An orthonormal tetrad system and associated coordinate system is obtained, which may be used to locally describe any dust‐filled space‐time. This is used to study dust‐filled spaces in which there exist multiply transitive groups of motions; all such spaces are classified in detail. Spaces containing shear‐free dust are also considered; it is shown that σ = 0 ⇒ ωΘ = 0. Three classes of solution with σ = 0, ω ≠ 0 are studied. Several new solutions of the field equations are contained in these results.
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TL;DR: The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field and a quick reference to recent results and constraints on testing gravity at cosmological scales.
Abstract: We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.
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Cites background from "Spherically Symmetrical Models in G..."
...These include, for example, the isotropic and homogeneous Friedmann–Lemaître–Robertson–Walker (FLRW) solutions (Friedmann 1922; Lemaître 1931; Robertson 1935; Walker 1937), the inhomogeneousLemaître–Tolman–Bondi solutions (Lemaître 1933; Tolman 1934; Bondi 1947), the inhomogeneous Szekeres models (Szekeres 1975), the anisotropic Bianchi models (Ellis and MacCallum 1969), and others (Ellis and van Elst 1999)....
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...…(Friedmann, 1922; Lemaitre, 1931; Robertson, 1935; Walker, 1937), the inhomogeneous Lemâıtre-Tolman-Bondi solutions (Lemaitre, 1933; Tolman, 1934; Bondi, 1947), the inhomogeneous Szekeres models (Szekeres, 1975), the anisotropic Bianchi models (Ellis and MacCallum, 1969), and others (Ellis…...
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