Re-Examination of Globally Flat Space-Time

Abstract

In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of “dark energy,” “dark matter,” and “dark flow.” Instead of assuming the existence of these theoretical concepts, we take an alternative route and choose to redefine what we consider to be inertial motion as well as what constitutes an inertial frame of reference in flat space-time. We adopt none of the features of our current cosmological models except for the requirement that special and general relativity be local approximations within our revised definition of inertial systems. Implicit in our ideas is the assumption that at “large enough” scales one can treat objects within these inertial systems as point-particles having an insignificant effect on the curvature of space-time. We then proceed under the assumption that time and space are fundamentally intertwined such that time- and spatial-translational invariance are not inherent symmetries of flat space-time (i.e., observable clock rates depend upon both relative velocity and spatial position within these inertial systems) and take the geodesics of this theory in the radial Rindler chart as the proper characterization of inertial motion. With this commitment, we are able to model solely with inertial motion the observed effects expected to be the result of “dark energy,” “dark matter,” and “dark flow.” In addition, we examine the potential observable implications of our theory in a gravitational system located within a confined region of an inertial reference frame, subsequently interpreting the Pioneer anomaly as support for our redefinition of inertial motion. As well, we extend our analysis into quantum mechanics by quantizing for a real scalar field and find a possible explanation for the asymmetry between matter and antimatter within the framework of these redefined inertial systems.

Weyl conformastatic perihelion advance

“…It is worth noting that the original paper of Weyl showed that the cylinder solution is diffeomorphic to a Schwarzschild's solution. In this process the metric does not lose its asymptotes as shown in (Weyl 1917;Rosen 1949;Zipoy 1966) and is also asymptotically flat (Weyl 1917;Rosen 1949;Zipoy 1966;Gautreau, Hoffman and Armenti 1972;Stephani et al 2003). This is a fine example of the equivalence problem in GR: How do we know that two solutions of Einstein's equations, written in different coordinates, do not describe the same gravitational field?…”

“…In this ⋆ E-mail:abraao.capistrano@unila.edu.br † E-mail:roque@ci.ufbp.br ‡ E-mail:rafaelsvalada@ulbra.edu.br respect, we use the Weyl metric that describes a cylindrical symmetry, motivated mainly on the fact that the solar system has an axial symmetry. From the geometrical point of view the Weyl cylindrically symmetric solution is diffeomorphic to the Schwarzschild solution and also is asymptotically flat as shown in (Weyl 1917;Rosen 1949;Zipoy 1966;Gautreau, Hoffman and Armenti 1972;Stephani et al 2003). For applications in astrophysics, the Weyl metric is fundamentally relevant as well as several non-asymptotically flat metrics, for instance, in the study of physics of black-holes, stellar evolution and galaxies as well as several studies of relativistic effects on solar system scale (Gutiérrez-Piñeres, González and Quevedo 2013;González, Gutiérrez-Piñeres and Ospina 2008;Katz, Bicák and Lynden-Bell 1999;Vogt and Letelier 2008;Ujevic andLetelier 2004, 2007;Sitarski 1983;Roberts 1987).…”

“…In recent years there has been a renewed interest in the perihelion advance and several proposals have been worked using it as one of the fundamental solar system tests, such as, e.g, the modification of Newtonian Dynamics (MOND)(Schmidt 2008), azimuthally symmetric theory of gravitation based on the study of Poisson equation (Nambuya 2010), Kaluza-Klein five-dimensional gravity (Lim and Wesson 1992), Yukawa-like Modified Gravity (Iorio 2008a), Horava-Lifshitz gravity (Harko et al 2011), brane-world models and variants (Mak and Harko 2004;Cheung and Xu 2013;Chakraborty and Sengupta 2014;Jalalzadeh et al 2009;Iorio 2009a,b) and also in the PPN framework and outside it giving rise to extra-perihelion precessions and approaches in the weak field/slow motion limits (Avalos-Vargas and Ares de Parga 2012; Arakida 2013; Adkins and McDonnell 2007;D'Eliseo 2012;Deng and Xie 2014;Feldman 2013;Kalinowski 2013;Liang and Xie 2014;Li et al 2014;Iorio 2005Iorio , 2006Iorio , 2008bIorio , 2011Iorio , 2012aIorio ,b,c, 2013aIorio ,b, 2014aRuggiero 2014;Xie and Deng 2014;Wilhelm and Dwivedi 2014).…”

On the possible onset of the Pioneer anomaly

“…Furthermore, Ref. 43 takes the Milky Way itself to constitute one of these new inertial frames with the center of the Milky Way in the direction of Sagittarius A* constituting the center of the inertial reference frame relevant for observers in our Solar System. In other words, it is assumed in this model that at the center of our galaxy there exists an inertial center and not a supermassive black hole (for recent tension with our current understanding of black hole formation, see Refs.…”

Effective apsidal precession from a monopole solution in a Zipoy spacetime

“…Since the explanation of the perihelion advance of Mercury by Einstein in 1915 as an application of general Relativity (GR), it has been considered one of the fundamental laboratories for testing extensions of standard GR and other gravitational models such as e.g, the modification of newtonian Dynamics (MOND) [2], Kaluza-Klein five-dimensional gravity [3], Yukawa-like Modified Gravity [4], Horava-Lifshitz gravity [5], brane-world models and variants [6][7][8][9][10][11][12], the parametric post-newtonian (PPN) framework and beyond, and approaches in the weak field/slow motion limits [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. As largely known, in GR, the coordinate systems are overall physically equivalents and to obtain new prospects on applications in astrophysics, the diffeomorphic a e-mail: abecapistrano@gmail.com b e-mail: paola.seidel@gmail.com c e-mail: cabral@uft.edu.br transformations cannot be allowed to happen.…”