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Local and Global Flatness in Cosmology

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Journal of Modern Physics 2019年第12期10卷 1439-1453页

作者： Rainer Burghardt A-2061 obritz 246 Obritz Austria

We raise the question of how the curvature parameter k is related to the curvature of the universe. We also show that, for a cosmological model that can be interpreted geometrically as a pseudo-hypersphere with a time-dependent radius, the Einstein field equations are not sufficient to fully describe the model. In addition, the differential equation system of Bianchi identities is required to describe the temporal evolution of the universe. We discuss the facts using the example of the de Sitter universe, the subluminal universe and the Rh=ct model by Melia. In particular, we discuss the formal differences between the two latter models and claim that both models are identical. We also examine the possibility of introducing non-comoving coordinates.

关键词： Curvature Parameter Bianchi Identities de Sitter Cosmos Subluminal Cosmos Rh=ct Cosmos Geometric Horizon

Linking Conditions for Models with Geometrical Basis

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Journal of Modern Physics 2020年第3期11卷 355-364页

作者： Rainer Burghardt A-2061 obritz 246 Obritz Austria

Usually it is demanded that the metric and its 1st derivatives have to match at the boundary of two adjacent regions which are solutions to Einstein’s field equation. We propose a new linking condition concerning gravitational models based on surfaces which could be embedded into a higher dimensional flat space. We probe this condition for the Schwarzschild interior and exterior solution.

关键词： Linking Conditions Short Discussions of Previous Papers Schwarzschild Models Flamm’ Paraboloid

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Drawing Kerr

Journal of Modern Physics 2019年第5期10卷 515-538页

作者： Rainer Burghardt A-2061 obritz 246 Obritz Austria

The Kerr metric is analyzed using strictly geometrical elements. A 4-dimensional surface representing the geometry of the Kerr model is embedded into a 5-dimensional flat space. The field strengths of the model are explicitly worked out and understanding of the theory is supported by numerous figures. The structure of the field equations is analyzed.

关键词： Kerr Geometry Geometrical Interpretation Kerr Surface

Lemaître Transformations of the Interior Schwarzschild Metric

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Journal of Modern Physics 2021年第2期12卷 99-104页

作者： Rainer Burghardt A-2061 obritz 246 Obritz Austria

A Lemaître transformation is set up for the free fall in the interior of a stellar object using the frame of the interior Schwarzschild solution. The metric is calculated in comoving coordinates and field strengths ar... 详细信息

关键词： Interior Schwarzschild Metric Lemaître Transformations Freely Falling Systems

Melia’s R<sub>h</sub>= ct Model Is by No Means Flat

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Journal of Modern Physics 2020年第5期11卷 703-711页

作者： Rainer Burghardt A-2061 obritz 246 Obritz Austria

With the support of numerous arguments, it has been shown that Melia’s claim that his cosmological Rh = ct model is flat and infinite is erroneous. In contrast, the model is positively curved, closed and, therefore, ... 详细信息

关键词： Globally and Locally Flat Cosmos Melia’s Rh = ct Model Subluminal Model Curvature Parameter

Einstein’s Elevator in Cosmology

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Journal of Modern Physics 2016年第16期7卷 2347-2356页

作者： Rainer Burghardt obritz Austria

The metrics of gravitational and cosmological models are brought into canonical form in comoving coordinates. The FWR curvature parameter k is read from this and it is shown that k=0 does not correlate to a flat model, but for a spatially positively curved geometry in which reference systems which are in free fall exist. This also corresponds to Einstein’s elevator principle. Moreover, we will show that our subluminal cosmos is associated with the Rh=ct model of Melia, assuming that k=0 is related to a free-falling system in the sense described above.

关键词： Cosmology Einstein’s Elevator Canonical Form of the Metric

Generalization of the de Sitter Cosmos

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Journal of Modern Physics 2018年第4期9卷 685-700页

作者： Rainer Burghardt Independent Researcher Obritz Austria

First of all, we investigate whether the transformation of Lemaître inevitably leads from the static de Sitter cosmos to an expanding cosmos. A Lorentz transformation which can be assigned to the Lemaître transformation results in a frame of reference that moves relatively to the static dS system. Because of the homogeneity of space, this applies to every point in the space which does not itself undergo any change. We interpret the “expansion” of the cosmos Milne-like. It is not the space that expands, but the mesh of the Lemaître coordinate system. The velocity parameter of the associated Lorentz transformation is geometrically based and shows that the joined observer systems are moving in free fall. We also discuss the question of whether the speed of light for free-falling observers in the universe can be reached or can be exceeded, respectively. We raise the question of whether the model can be extended in such a way that the motions take place with a velocity that is lower than the one of the free fall. We believe that the method we have derived can be generalized to models with genuine expansion.

关键词： De Sitter Cosmos Accelerated Expansion Coordinate Transformations Reference-System Transformations

Collapsing Schwarzschild Interior Solution

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Journal of Modern Physics 2015年第13期6卷 1895-1907页

作者： Rainer Burghardt A-2061 obritz 246 Austria

We extend the static interior Schwarzschild solution to a collapsing model by applying geometrical methods. We examine the field quantities and field equations in the comoving and non-comoving observer systems. The collapsing stellar object contracts asymptotically to its minimum extent and needs an infinitely long time to arrive at the final state. The event horizon of the exterior Schwarzschild solution is not reached or even crossed. A geometric model of ECOs (eternally collapsing objects) is presented.

关键词： Collapse Interior Schwarzschild Solution Interior Horizon Comoving and Non-Comoving Reference Systems

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Subluminal Cosmology

Journal of Modern Physics 2017年第4期8卷 583-601页

作者： Rainer Burghardt Independent Researcher Obritz Austria

The standard model of cosmology is considered critically. A model with pressure is proposed which is linearly expanding and which is an exact solution of Einstein’s field equations. The recession velocity of the galaxies of this model never exceeds the speed of light. The model is closely related to the Rh=ct model of Melia, which is flat and infinite. However, our subluminal model is spatially positively curved and closed. Nevertheless all data from observations gathered and surveyed by Melia support our model.

关键词： Expanding Cosmos with Pressure Subluminal Expansion Covariant Representation