跳至主要内容

Minkowskian Solution of General Relativity with Cosmological Constant and the Accelerating Universe

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=51072#.VFMa_WfHRK0

Author(s)
A Minkowskian solution of the equation of General Relativity (as written by Einstein in 1915) is trivial because it simply means that both members of the equation are equal to zero. However, if alternatively, one considers the complete equation with a non-zero constant Λ (Einstein 1917), a Minkowskian solution is no longer trivial because it amounts to impose a constraint on the right hand side of the equation (i.e. a non-null stress-energy tensor). If furthermore one identifies (as usual) this tensor to the one of a perfect fluid, one finds that this fluid has a positive energy density and a negative pressure that depend on the three constants of the equation (i.e. gravitational constant G, cosmological constant Λ and velocity of light c). When doing that (§1), one has to consider the “Minkowskian Vacuum” as a physical object of GR (an enigmatic non-baryonic Minkowskian fluid). Can one build a model of this object on the basis of a dynamical equilibrium between the effective gravitational attraction due to the positive energy density versus the negative pressure repulsion? We propose to study such a model, where the (enigmatic) fluid is assumed to exist only in a limited sphere whose surface acts like a “test body” sensitive to the gravitational field created by the fluid. No static equilibrium exists, but a pseudoNewtonian “dynamical equilibrium” (§2) can be reached if the pseudoEuclidean fluid is in state of expansion. Up to there, we have simply constructed a model of an “abstract Universe” (i.e. the limited sphere: There is no fluid outside this sphere!) that gives to a (purely mathematical) constant Λ a concrete physical meaning. We discover finally that our expanding fluid has not only dynamical (gravitational) properties (§3) but also optical properties that are connected with Doppler Redshift (§4). Remembering that recent observations in Cosmology indicate that the “real Universe” seems to be “Flat” and in “Accelerated Expansion”; remembering also (after all) that the archetypal Flat Universe is simply a Minkowskian Universe, we logically wonder if the unexpected Minkowskian global solution, could not be also a significant cosmological model (conclusion).
Cite this paper
Pierseaux, Y. (2014) Minkowskian Solution of General Relativity with Cosmological Constant and the Accelerating Universe. Journal of Modern Physics, 5, 1725-1732. doi: 10.4236/jmp.2014.516172. 
 

[1] Einstein, A. (1916) Annalen der Physik, 354, 769-822.
[2] Einstein, A. (1917) Kosmologische Betrachtungen zur Allgemeinen Relativitatstheorie. In: Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften, VI, Berlin, 142-152.
[3] Poincare, H. (1906) Rendicontidel Circolo Matematico di Palermo, 21, 129-175.
[4] de Sitter, W. (1917) Royal Astronomical Society Monthly Notices, LXXVIII, 3-28.
http://dx.doi.org/10.1093/mnras/78.1.3
[5] Pierseaux, Y. (2010) From Unexpected Minkowskian Solution of Einstein’s Equation of General Relativity with Cosmological Constant to the Accelerating Universe. Revue IIHE.
http://arxiv.org/abs/1009.1375
[6] Rindler, W. (2001) Relativity. Special, General and Cosmological. Oxford University Press, Oxford.
[7] Einstein, A. (1905) Annalen der Physik, 17, 891-921.
[8] Bondi, H. (1962) Relativity and Common Sense. A New Approach to Einstein. Dover Publications Inc., New York.
[9] Pierseaux, Y. (2013) Annales de la Fondation Louis de Broglie, 38, 41-55.
[10] Riess, A., et al. (1998) Astronomical Journal, 116, 1009-1038.
http://dx.doi.org/10.1086/300499
[11] Peebles, P.J.E. (2002) The Cosmological Constant and Dark Energy.
http://arxiv.org/abs/astro-ph/0207347                      eww141031lx
[12] Turner, M. (2002) The New Cosmology. World Scientific, Singapore.
标签：

评论

发表评论

此博客中的热门博文

A Comparison of Methods Used to Determine the Oleic/Linoleic Acid Ratio in Cultivated Peanut (Arachis hypogaea L.)

Cultivated peanut ( Arachis hypogaea L.) is an important oil and food crop. It is also a cheap source of protein, a good source of essential vitamins and minerals, and a component of many food products. The fatty acid composition of peanuts has become increasingly important with the realization that oleic acid content significantly affects the development of rancidity. And oil content of peanuts significantly affects flavor and shelf-life. Early generation screening of breeding lines for high oleic acid content greatly increases the efficiency of developing new peanut varieties. The objective of this study was to compare the accuracy of methods used to classify individual peanut seed as high oleic or not high oleic. Three hundred and seventy-four (374) seeds, spanning twenty-three (23) genotypes varying in oil composition (i.e. high oleic (H) or normal/not high oleic (NH) inclusive of all four peanut market-types (runner, Spanish, Valencia and Virginia), were individually tested ...
发表评论
阅读全文

Location Optimization of a Coal Power Plant to Balance Costs against Plant’s Emission Exposure

Fuel and its delivery cost comprise the biggest expense in coal power plant operations. Delivery of electricity from generation to consumers requires investment in power lines and transmission grids. Placing a coal power plant or multiple power plants near dense population centers can lower transmission costs. If a coalmine is nearby, transportation costs can also be reduced. However, emissions from coal plants play a key role in worsening health crises in many countries. And coal upon combustion produces CO 2 , SO 2 , NO x , CO, Metallic and Particle Matter (PM10 & PM2.5). The presence of these chemical compounds in the atmosphere in close vicinity to humans, livestock, and agriculture carries detrimental health consequences. The goal of the research was to develop a methodology to minimize the public’s exposure to harmful emissions from coal power plants while maintaining minimal operational costs related to electric distribution losses and coal logistics. The objective was...
发表评论
阅读全文

Evaluation of the Safety and Efficacy of Continuous Use of a Home-Use High-Frequency Facial Treatment Appliance

At present, many home-use beauty devices are available in the market. In particular, many products developed for facial treatment use light, e.g., a flash lamp or a light-emitting diode (LED). In this study, the safety of 4 weeks’ continuous use of NEWA TM , a high-frequency facial treatment appliance, every alternate day at home was verified, and its efficacy was evaluated in Japanese individuals with healthy skin aged 30 years or older who complained of sagging of the facial skin.  Transepidermal water loss (TEWL), melanin levels, erythema levels, sebum secretion levels, skin color changes and wrinkle improvement in the facial skin were measured before the appliance began to be used (study baseline), at 2 and 4 weeks after it had begun to be used, and at 2 weeks after completion of the 4-week treatment period (6 weeks from the study baseline). In addition, data obtained by subjective evaluation by the subjects themselves on a visual analog scale (VAS) were also analyzed. Fur...
发表评论
阅读全文