1,668 research outputs found
The Possibility of a Non-Lagrangian Theory of Gravity
General Relativity resembles a very elegant crystal glass: If we touch its
principles, that is, its Lagrangian, there is a risk of breaking everything.
Or, if we will, it is like a short blanket: Curing some problems creates new
problems. This paper is devoted to bring to light the reasons why we pursue the
possibility of a non-Lagrangian theory of gravity under the hypothesis of an
extension of the original general relativity with an ansatz inspired in the
fundamental principles of classical and quantum physics.Comment: 6 pages, 1 figure. Version accepted in Universe MDP
Poincar\'e's polyhedron theorem for cocompact groups in dimension 4
We prove a version of Poincar\'e's polyhedron theorem whose requirements are
as local as possible. New techniques such as the use of discrete groupoids of
isometries are introduced. The theorem may have a wide range of applications
and can be generalized to the case of higher dimension and other geometric
structures. It is planned as a first step in a program of constructing compact
-surfaces of general type satisfying .Comment: 15 pages, 1 figure, 9 references. Introduction revised. Example 3.16
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Modified gravity models and the central cusp of dark matter haloes in galaxies
The N-body dark matter (DM) simulations point that DM density profiles, e.g. the Navarro Frenk White (NFW) halo, should be cuspy in its centre, but observations disfavour this kind of DM profile. Here we consider whether the observed rotation curves close to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, Modified Newtonian Dynamics (MOND) and a more recent approach renormalization group effects in general relativity (RGGR). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches. By analysing 62 galaxies from five samples, we find that (i) there is a radius, given by half the disc scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; (ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have, respectively, two and one more free parameters than MOND)
Renormalization Group approach to Gravity: the running of G and L inside galaxies and additional details on the elliptical NGC 4494
We explore the phenomenology of nontrivial quantum effects on low-energy
gravity. These effects come from the running of the gravitational coupling
parameter G and the cosmological constant L in the Einstein-Hilbert action, as
induced by the Renormalization Group (RG). The Renormalization Group corrected
General Relativity (RGGR model) is used to parametrize these quantum effects,
and it is assumed that the dominant dark matter-like effects inside galaxies is
due to these nontrivial RG effects. Here we present additional details on the
RGGR model application, in particular on the Poisson equation extension that
defines the effective potential, also we re-analyse the ordinary elliptical
galaxy NGC 4494 using a slightly different model for its baryonic contribution,
and explicit solutions are presented for the running of G and L. The values of
the NGC 4494 parameters as shown here have a better agreement with the general
RGGR picture for galaxies, and suggest a larger radial anisotropy than the
previously published result.Comment: 9 pages, 2 figs. Based on a talk presented at the VIII International
Workshop on the Dark Side of the Universe, June 10-15, 2012, Buzios, RJ,
Brazil. v2: typos removed, matches published versio
Some Remarks on Alternative (or Modified) Theories of Gravity
A seminar given about 30 years ago by Ruben Aldrovandi motivates this text
where some reflexions about constructing theories that modify General
Relativity are made. Two particular cases, the Brans-Dicke and Unimodular
Gravity ones, are discussed, in a quite qualitative way, showing on how they
can address some of the most outstanding problems of General Relativity,
specially the transplanckian physics and the cosmological constant problem.Comment: Latex file, 14 pages. To appear in the volume "Tribute to Ruben
Aldrovandi" (Editora Livraria da F\'isica, S\~ao Paulo, 2024
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