Authors:Michel Canac Abstract: Reports in Advances of Physical Sciences, Volume 07, Issue , 2023. Birkhoff’s theorem (1923) states that in the framework of General Relativity the only solution to the central symmetric gravitational field in vacuum is the Schwarzschild metric. This result has crucial consequences in the resolution of the dark matter problem. This problem can only be solved through the discovery of a new type of matter particles, or by the introduction of a new theory of gravitation which supplants General Relativity. After reviewing Birkhoff’s theorem, it was discovered that by starting the calculation of the metric from an indeterminate metric whose coefficients are locally defined, we obtain a solution containing two arbitrary functions. In general, these functions do not induce any difference between this solution and the Schwarzschild metric. However, it can be seen that if we choose a triangular signal for these functions, the situation changes dramatically: (1) the metric is broken down into four distinct metrics that replace each other cyclically over time, (2) for two of these four metrics, the coordinate differentials dr and dt switch their spatial/temporal role cyclically, (3) the four metrics are not separable: they form a single logical set that we call a 4-metric and (4) this 4-metric cannot be transformed into the Schwarzschild metric by any coordinate change. According to these findings, there is a second solution in the spherical space, in addition to the Schwarzschild metric, and thus, Birkhoff’s theorem is incomplete. In the 4-metric, the orbital velocity of a massive particle does not depend on the radial distance. This 4-metric is thus in agreement with the baryonic Tully–Fisher relation (BTFR), (consequently BTFR is in agreement with a solution of General Relativity without presence of dark matter and without hypothesis on the distribution of stars in galaxies). By combining the 4-metric with the Schwarzschild metric, another 4-metric in agreement with the observed galaxy rotation curve can been obtained. The calculation of the light deflection in this space is also exposed in this paper. According to these findings: (1) it is not necessary to introduce the notion of dark matter or the notion of distribution of stars in galaxies in order to find the observed galaxy rotation curve in the framework of General Relativity, (2) the modification of the metric with respect to the Schwarzschild metric appears to be due to the existence of a lower bound of the space-time curvature in galaxies (without external field effect), this phenomenon leading to a temporal oscillation of the space-time curvature, (3) an analysis of the external field effect for the Milky Way-Andromeda couple allows to model the rotation curve of the two galaxies beyond the plateau zone. The validation of these findings would be the first step toward challenging the standard model of cosmology ([math]CDM), as the [math]CDM model cannot be in agreement with the observed galaxy rotation curve without presence of dark matter. The second step would be the demonstration that there is no dark matter in intergalactic spaces (not included in this paper). Citation: Reports in Advances of Physical Sciences PubDate: 2023-04-28T07:00:00Z DOI: 10.1142/S2424942423500020 Issue No:Vol. 07 (2023)
Authors:Dale. R. Koehler Abstract: Reports in Advances of Physical Sciences, Volume 07, Issue , 2023. It is shown in this paper that the distorted space model of matter can describe a universe transitioning between conception and an open-ended finality. We use the verbiage “distorted” to communicate the concept of “energetic-manifold-warping” and to distinguish “spatial-warping” from “classical matter-warping”, although the concept of “matter” is in fact, in the present “distorted-geometry” context, the “geometric distortion energy” of the spatial manifold itself without a classical “matter stress-energy source”. An energy conserving alternative to black-body radiation-emission structural-modeling is manifest as an energetically unstable Universe (an originally stable but subsequently collapsing state, followed by an explosive expansion, thereby exhibiting an energy-creation process of one day!). The energy transition dynamics are described for a spherical, gravitational, and electromagnetic, geometrically-based mimic of matter existing at quantitative measures of a size challenging observation, that is, at a calculated Universe (gravitational body) [math] m and [math] J. The Universe (electromagnetic body) radius is calculated [math] m. We have modeled the structure with a composite, two-component, geometric-coupling_constant and initial structural conditions representing Friedmann’s critical density, [math]_critical energy-density (8.898[math] J/m3) for the gravitational energy-density and [math]_electron (8.7[math] J/m3) [math] the [math]_critical energy-density for the geometric-electromagnetic extremum; the geometric extrema are curvature and energy-density extrema. A collapsing initial-phase-1 state, posited as a Friedmann-defined, distorted-geometry (DG) configuration with two equal-energy species or energy-density states, transitions electromagnetically, via an intermediate “mediator or force carrier” state (a W-boson structure in beta-decay), to a final 3-component state (ala a mimic of the beta decay transition process). Citation: Reports in Advances of Physical Sciences PubDate: 2023-04-28T07:00:00Z DOI: 10.1142/S2424942423500032 Issue No:Vol. 07 (2023)
Authors:P. D. Morley Abstract: Reports in Advances of Physical Sciences, Volume 07, Issue , 2023. The scalar curvature [math] is invariant under isometric symmetries (distance invariance) associated with metric spaces. Gravitational Riemannian manifolds are metric spaces. For Minkowski Space, the distance invariant is [math], where [math], [math] are arbitrary 4-vectors. Thus the isometry symmetry associated with Minkowski Space is the Poincaré Group. The Standard Model Lagrangian density [math] is also invariant under the Poincaré Group, so for Minkowski Space, the scalar curvature and the Standard Model Lagrangian density are proportional to each other. We show that this proportionality extends to general gravitational Riemannian manifolds, not just for Minkowski Space. This predicts that Black Holes have non-zero scalar curvatures [math]. For Schwarzschild Black Holes, [math] is predicted to be [math], where [math] is the Schwarzschild radius. The existence of [math] means that Black Holes cannot evaporate. Citation: Reports in Advances of Physical Sciences PubDate: 2023-04-22T07:00:00Z DOI: 10.1142/S2424942423500019 Issue No:Vol. 07 (2023)
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