A projective approach to dynamical systems, applications in cosmology and connections with El Naschie ϵ(∞) Cantorian space–time

Iovane, Gerardo; Benedetto, Elmo

doi:10.1016/j.chaos.2005.11.005

Cited by 9 publications

(3 citation statements)

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“…Other motivations come from the Mach's Principle, that played an important role in the development of General Relativity, as, for example, the Brans-Dicke theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of General Relativity and the gravitational constant G is not presumed to be constant but instead 1/G is replaced by a scalar field which can vary from place to place and with time. Another theory in accord with Mach's Principle is de Sitter Relativity initially proposed by Fantappié and subsequently developed by Arcidiacono and other authors [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. At present, both Brans-Dicke theory and de Sitter Relativity are generally held to be in agreement with observation.…”

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confidence: 74%

Brief History of a Relativistic Century

Benedetto

2011

Int J Theor Phys

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More than one century is passed by the publication of special relativity and few less by the birth of general relativity. Despite the great experimental successes of these theories, the study of the universe, is plagued by numerous unsolved problems. For example one of the most problems in cosmology is the cosmological constant, which governs the expansion of the universe, also known as dark energy. A substantial portion, about 60%, of the mass-energy in the universe is in a form of mysterious energy that is pushing the cosmos apart at an accelerating rate. What is this energy, and where does it come from? Cosmologists have no real idea. Although given a similar name, there is another problem in cosmology, the so-called dark matter, which is actually unrelated to dark energy, except insofar as they involve things we don't understand. About 90% of the mass in the universe is in an apparently invisible form of matter that we call dark matter. This dark matter can only be measured by the gravitational pull it has on objects around it, and all galaxies we observe contain large halos of it, often extending for hundreds of thousands of light years beyond the edge of luminous matter. Is this dark matter actual matter, such as weakly interacting massive particles, or perhaps it is just an observational artifact caused by an improper theory of gravity? Another mystery is why there is so much more matter than antimatter in the universe. According to physical theories, these forms of matter are essentially equivalent, but conventional matter is observed in much greater abundances than antimatter. In this paper we summarily introduce the principal alternative theories proposed during one century of relativity.

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confidence: 74%

Brief History of a Relativistic Century

Benedetto

2011

Int J Theor Phys

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“…In [21] we considered the dynamical properties of projective spacetime and we shortly resume the gotten results. The projective 4-velocity is defined by the following relation…”

Section: Projective Dynamicsmentioning

confidence: 99%

“…Fantappié noted that general relativity follows an approach far from the tradition of mathematical physics in that it does not follow the group structure of physics [4]. Subsequently this theory has been developed by Arcidiacono [5][6][7][8][9][10][11][12][13][14][15] and during the years also other authors have shown interest for this approach to cosmology [16][17][18][19][20][21][22][23]. As it is known, minor changes to the Einstein equations, while exhibiting all the classical verifications, produce completely different cosmologically-interesting solutions and possible universes are numerous.…”

Section: Introductionmentioning

confidence: 99%

Fantappié-Arcidiacono Spacetime and Its Consequences in Quantum Cosmology

Benedetto

2009

Int J Theor Phys

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Einstein's gravitational theory gave rise to a new conception of the Universe and Cosmology has been enclosed in the realm of Science and not only of Philosophy as before the Einstein work. Despite this, the presence of the Big Bang singularity, flatness and horizon problems led to the statement that Standard Cosmological Model, based on General Relativity and Standard Model of particle physics, is inadequate to describe the Universe in extreme regimes. Due to this facts, alternative gravitational theories and alternative approaches to cosmology have been proposed during the years. One of the most fruitful approach has been that of Projective Relativity and, in this paper, we analyze the developments of this theory. Projective Relativity, initially proposed by Fantappié and subsequently developed by Arcidiacono, has been recently revisited by prof. Ignazio Licata and other authors. The cosmological consequences of such extension appear relevant. In the following, we analyze the effects of the group approach on the metrics and on the dynamics and we will consider its properties in connection with varying speed of light.

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