Rainer Burghardt - Academia.edu (original) (raw)

Papers by Rainer Burghardt

Research paper thumbnail of Kretschmann scalar and black holes

Austrian Reports on Gravitation, 2024

We demonstrate that the Kretschmann scalar cannot be applied to the region r < 2M of the exterior... more We demonstrate that the Kretschmann scalar cannot be applied to the region
r < 2M of the exterior Schwarzschild solution.

Research paper thumbnail of Anholonomy and rotating systems

Austrian Reports on Gravitation, 2024

We study the conditions under which the conservation law is satisfied for a rotating elliptical m... more We study the conditions under which the conservation law is satisfied for a rotating elliptical model, with particular attention to the anholonomic effects that arise from implementing rotation. Contents

Research paper thumbnail of Expansion scalar in cosmology

Austrian Reports on Gravitation, 2024

We examine the expansion scalar of the dS model and the Subluminal Model. If the expansion scalar... more We examine the expansion scalar of the dS model and the Subluminal Model. If the expansion scalar vanishes in the non-comoving system, the model is static and the comoving metric describes a motion of diverging observer systems.

Research paper thumbnail of Visualizing the de Sitter forces

Austrian Reports on Gravitation, 2024

We will show that as the consequence of the homogeneity of the universe the forces of the dS cosm... more We will show that as the consequence of the homogeneity of the universe the forces of the dS cosmos are repulsive at all points in space and cancel each other out.Thus, no expansion is possible.

Research paper thumbnail of An interesting property of the Kerr metric

We show that the Einstein tensor of the Kerr model can be represented in two parts, one originati... more We show that the Einstein tensor of the Kerr model can be represented in two parts, one originating from the static elliptical geometry and the second describing the rotational part, which is attached to the static part by an anholonomic transformation. Contents

Research paper thumbnail of Geometrical  foundation of the equation of state in cosmological models

Austrian Reports in Gravitation, 2024

This study demonstrates that the equation of state (EOS) of an expanding cosmological model is de... more This study demonstrates that the equation of state (EOS) of an expanding cosmological model is derivable from the geometrical properties of the model. We do this using our Subluminal Model, which is geometrically based on a pseudo-hypersphere.

Research paper thumbnail of Penrose metric and black holes

Austrian Reports on Gravitation, 2023

The Penrose metric is investigated, and it is shown that it cannot describe the inner region of t... more The Penrose metric is investigated, and it is shown that it cannot describe the inner region of the Schwarzschild model. It cannot represent a black hole.

Research paper thumbnail of Black hole metric is massless

Austrian Reports on Gravitation, 2023

In this paper, we show that black hole metric is massless and cannot be used to describe black ho... more In this paper, we show that black hole metric is massless and cannot be used to describe black holes. Moreover, in earlier studies, we showed that a stellar object cannot collapse beyond the event horizon, i.e., cannot collapse to a black hole. Contents

Research paper thumbnail of Geometry and Cosmology

To describe cosmological models, we use geometric methods based on embeddings of class one. The m... more To describe cosmological models, we use geometric methods based on embeddings of class one. The models we study are positively curved and closed and are based on a pseudo-hypersphere. Contents

Research paper thumbnail of Equipping the model of Melia with curvature

Austrian Reports on Gravitation, 2023

We compare Melia's R h =ct model with our Subluminal Model and conclude that both are positively ... more We compare Melia's R h =ct model with our Subluminal Model and conclude that both are positively curved and finite. We use the 2 nd fundamental forms to formulate the field equation of these models. Contents

Research paper thumbnail of Coordinate systems, reference systems, black holes, ECOs, and cosmological problems

Austrian Reports on Gravitation, 2023

In this paper we intend to show that the search for new coordinates to penetrate the event horizo... more In this paper we intend to show that the search for new coordinates to penetrate the event horizon of the Schwarzschild model, is hopeless. We also show that the formation of Black Holes is impossible in the framework of the complete Schwarzschild model, consisting of the exterior and interior solutions. In addition, we make some critical remarks about coordinate systems in cosmology.

Research paper thumbnail of Covariant variational principle in the theory of gravitation

Annalen der Physik , 1987

Gravitation theory treated in Treder's version of Lorentz space is supplemented by a coordinate i... more Gravitation theory treated in Treder's version of Lorentz space is supplemented by a coordinate invariant variation principle.

Research paper thumbnail of The interior of an elliptic stellar object

Austrian Reports on Gravitation, 2022

An elliptic-hyperbolic static model is established - a model that can be applied as a source for ... more An elliptic-hyperbolic static model is established - a model that can be applied as a source for a gravitational field. Field equations as curvature equations of the geometry are presented. We find relations to the Kerr geometry.

Research paper thumbnail of Anholonomy and gravitation

Austrian Reports on Gravitation, 2022

Riemannian geometry is extended with anholonomic structures to provide the possibility to explain... more Riemannian geometry is extended with anholonomic structures to provide the possibility to explain the geometrical properties of some gravitational models. Contents 1. Introduction 1 2. The methods 2 3. A simple example 4 4. Possible physical applications 6 5. Conclusions 8 6. References 8

Research paper thumbnail of Gravitational collapse: an overview

Austrian Reports on Gravitation, 2022

We investigate classical and newer models that describe a gravitational collapse. In our previous... more We investigate classical and newer models that describe a gravitational collapse. In our previous work, we examined well-known models using mathematical methods based on the use of rods and clocks. As a result, we obtained coordinate-invariant equations, which, however, revealed some contradictions. We also discuss in detail the possibility of black holes and singularity formation. Contents

Research paper thumbnail of Hybrid cosmological models

Austrian Reports on Gravitation, 2021

We show that some of the FRW models are hybrid models. In the hybrid case, spatial parts of the l... more We show that some of the FRW models are hybrid models. In the hybrid case, spatial parts of the line elements occur, which are typical for non-comoving systems, but the time in these models is the universal cosmological time-a comoving coordinate of a freely falling system. We investigate the line elements of models in the Florides metric and models in the Lemaître metric.

Research paper thumbnail of Subluminal  and superluminal universes

We compare a closed positive curved and an open negative curved expanding universe. The physical ... more We compare a closed positive curved and an open negative curved expanding universe. The physical velocities and the Hubble equation are calculated. We demonstrate that in an open universe, the physically defined velocities certainly exceed the velocity of light. In addition, we show that the recession velocities cannot be an effect of expansion of space but is an ordinary physical velocity. The open universes violate the principles of Special Relativity and are ruled out from being realized by Nature.

Research paper thumbnail of Flat or not flat, this is the question

Comparing Melia's R h =ct model and our Subluminal Model, regarding the flatness of both the models.

Research paper thumbnail of Comments on the use of the Flatness Theorem by Melia

Austrian Reports on Gravitation, 2021

We refer to a recently published paper by Melia concerning the Local Flatness Theorem. We argue t... more We refer to a recently published paper by Melia concerning the Local Flatness Theorem. We argue that Melia's claim that the timelike metrical coefficient gtt=1 is closely connected with the equation of state mu+3p=0 is based on a mathematical artifact. Melia's model is analyzed using coordinate independent methods and is compared with our Subluminal Model.

Research paper thumbnail of New Insights into Physical Science Vol. 1

Research paper thumbnail of Kretschmann scalar and black holes

Austrian Reports on Gravitation, 2024

We demonstrate that the Kretschmann scalar cannot be applied to the region r < 2M of the exterior... more We demonstrate that the Kretschmann scalar cannot be applied to the region
r < 2M of the exterior Schwarzschild solution.

Research paper thumbnail of Anholonomy and rotating systems

Austrian Reports on Gravitation, 2024

We study the conditions under which the conservation law is satisfied for a rotating elliptical m... more We study the conditions under which the conservation law is satisfied for a rotating elliptical model, with particular attention to the anholonomic effects that arise from implementing rotation. Contents

Research paper thumbnail of Expansion scalar in cosmology

Austrian Reports on Gravitation, 2024

We examine the expansion scalar of the dS model and the Subluminal Model. If the expansion scalar... more We examine the expansion scalar of the dS model and the Subluminal Model. If the expansion scalar vanishes in the non-comoving system, the model is static and the comoving metric describes a motion of diverging observer systems.

Research paper thumbnail of Visualizing the de Sitter forces

Austrian Reports on Gravitation, 2024

We will show that as the consequence of the homogeneity of the universe the forces of the dS cosm... more We will show that as the consequence of the homogeneity of the universe the forces of the dS cosmos are repulsive at all points in space and cancel each other out.Thus, no expansion is possible.

Research paper thumbnail of An interesting property of the Kerr metric

We show that the Einstein tensor of the Kerr model can be represented in two parts, one originati... more We show that the Einstein tensor of the Kerr model can be represented in two parts, one originating from the static elliptical geometry and the second describing the rotational part, which is attached to the static part by an anholonomic transformation. Contents

Research paper thumbnail of Geometrical  foundation of the equation of state in cosmological models

Austrian Reports in Gravitation, 2024

This study demonstrates that the equation of state (EOS) of an expanding cosmological model is de... more This study demonstrates that the equation of state (EOS) of an expanding cosmological model is derivable from the geometrical properties of the model. We do this using our Subluminal Model, which is geometrically based on a pseudo-hypersphere.

Research paper thumbnail of Penrose metric and black holes

Austrian Reports on Gravitation, 2023

The Penrose metric is investigated, and it is shown that it cannot describe the inner region of t... more The Penrose metric is investigated, and it is shown that it cannot describe the inner region of the Schwarzschild model. It cannot represent a black hole.

Research paper thumbnail of Black hole metric is massless

Austrian Reports on Gravitation, 2023

In this paper, we show that black hole metric is massless and cannot be used to describe black ho... more In this paper, we show that black hole metric is massless and cannot be used to describe black holes. Moreover, in earlier studies, we showed that a stellar object cannot collapse beyond the event horizon, i.e., cannot collapse to a black hole. Contents

Research paper thumbnail of Geometry and Cosmology

To describe cosmological models, we use geometric methods based on embeddings of class one. The m... more To describe cosmological models, we use geometric methods based on embeddings of class one. The models we study are positively curved and closed and are based on a pseudo-hypersphere. Contents

Research paper thumbnail of Equipping the model of Melia with curvature

Austrian Reports on Gravitation, 2023

We compare Melia's R h =ct model with our Subluminal Model and conclude that both are positively ... more We compare Melia's R h =ct model with our Subluminal Model and conclude that both are positively curved and finite. We use the 2 nd fundamental forms to formulate the field equation of these models. Contents

Research paper thumbnail of Coordinate systems, reference systems, black holes, ECOs, and cosmological problems

Austrian Reports on Gravitation, 2023

In this paper we intend to show that the search for new coordinates to penetrate the event horizo... more In this paper we intend to show that the search for new coordinates to penetrate the event horizon of the Schwarzschild model, is hopeless. We also show that the formation of Black Holes is impossible in the framework of the complete Schwarzschild model, consisting of the exterior and interior solutions. In addition, we make some critical remarks about coordinate systems in cosmology.

Research paper thumbnail of Covariant variational principle in the theory of gravitation

Annalen der Physik , 1987

Gravitation theory treated in Treder's version of Lorentz space is supplemented by a coordinate i... more Gravitation theory treated in Treder's version of Lorentz space is supplemented by a coordinate invariant variation principle.

Research paper thumbnail of The interior of an elliptic stellar object

Austrian Reports on Gravitation, 2022

An elliptic-hyperbolic static model is established - a model that can be applied as a source for ... more An elliptic-hyperbolic static model is established - a model that can be applied as a source for a gravitational field. Field equations as curvature equations of the geometry are presented. We find relations to the Kerr geometry.

Research paper thumbnail of Anholonomy and gravitation

Austrian Reports on Gravitation, 2022

Riemannian geometry is extended with anholonomic structures to provide the possibility to explain... more Riemannian geometry is extended with anholonomic structures to provide the possibility to explain the geometrical properties of some gravitational models. Contents 1. Introduction 1 2. The methods 2 3. A simple example 4 4. Possible physical applications 6 5. Conclusions 8 6. References 8

Research paper thumbnail of Gravitational collapse: an overview

Austrian Reports on Gravitation, 2022

We investigate classical and newer models that describe a gravitational collapse. In our previous... more We investigate classical and newer models that describe a gravitational collapse. In our previous work, we examined well-known models using mathematical methods based on the use of rods and clocks. As a result, we obtained coordinate-invariant equations, which, however, revealed some contradictions. We also discuss in detail the possibility of black holes and singularity formation. Contents

Research paper thumbnail of Hybrid cosmological models

Austrian Reports on Gravitation, 2021

We show that some of the FRW models are hybrid models. In the hybrid case, spatial parts of the l... more We show that some of the FRW models are hybrid models. In the hybrid case, spatial parts of the line elements occur, which are typical for non-comoving systems, but the time in these models is the universal cosmological time-a comoving coordinate of a freely falling system. We investigate the line elements of models in the Florides metric and models in the Lemaître metric.

Research paper thumbnail of Subluminal  and superluminal universes

We compare a closed positive curved and an open negative curved expanding universe. The physical ... more We compare a closed positive curved and an open negative curved expanding universe. The physical velocities and the Hubble equation are calculated. We demonstrate that in an open universe, the physically defined velocities certainly exceed the velocity of light. In addition, we show that the recession velocities cannot be an effect of expansion of space but is an ordinary physical velocity. The open universes violate the principles of Special Relativity and are ruled out from being realized by Nature.

Research paper thumbnail of Flat or not flat, this is the question

Comparing Melia's R h =ct model and our Subluminal Model, regarding the flatness of both the models.

Research paper thumbnail of Comments on the use of the Flatness Theorem by Melia

Austrian Reports on Gravitation, 2021

We refer to a recently published paper by Melia concerning the Local Flatness Theorem. We argue t... more We refer to a recently published paper by Melia concerning the Local Flatness Theorem. We argue that Melia's claim that the timelike metrical coefficient gtt=1 is closely connected with the equation of state mu+3p=0 is based on a mathematical artifact. Melia's model is analyzed using coordinate independent methods and is compared with our Subluminal Model.

Research paper thumbnail of New Insights into Physical Science Vol. 1

Research paper thumbnail of Zur Frage der Raumkrümmung

Austrian Reports on Gravitation, 2007

Den in dieser kurzen Abhandlung dargelegten Fortschritt auf dem Arbeitsgebiet 'Gravitationsmodell... more Den in dieser kurzen Abhandlung dargelegten Fortschritt auf dem Arbeitsgebiet 'Gravitationsmodelle' verdanke ich dem engen wissenschaftlichen Kontakt mit H.-J. Treder. In fast zweihundert Briefen gab es Anregungen und auch konstruktive Kritik, die mich auf dem manchmal holprigen Weg zur Lösung zahlreicher Probleme weitergeführt haben.

Research paper thumbnail of Karl Schwarzschild and what happened with his work

The gravitational model of Schwarzschild and attempts to generalize it. Soon after Einstein had... more The gravitational model of Schwarzschild and attempts to generalize it.
Soon after Einstein had published the first paper on the general theory of relativity, Karl Schwarzschild proposed two solutions of Einstein's field equations to describe the exterior and interior of a stellar object. It is certainly of interest to investigate how these solutions were dealt with in the course of a century and to discuss these results critically.

Research paper thumbnail of Spacetime Curvature 2024

Austrian Reports on Gravitation, 2024

8th extended edition

Research paper thumbnail of Raumkrümmung 2024

Austrian Reports on Gravitation, 2024

8. erweiterte Auflage

Research paper thumbnail of Raumkrümmung 2023

Austrian Reports on Gravitation, 2023