The kinetic gas universe

A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF). However, when the gravitational field of a kinetic gas is derived via the Einstein-Vlasov equations, the information about the velocity distribution of the gas particles is averaged out and therefore lost. We propose to derive the gravitational field of a kinetic gas directly from its 1PDF, taking the velocity distribution fully into account. We conjecture that this refined approach could possibly account for the observed dark energy phenomenology.Comment: 4 pages, Essay written for the Gravity Research Foundation competition 2020, Journal references update

On the gauge fixing in the Hamiltonian analysis of general teleparallel theories

The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads.Comment: 8 pages, no figures, Contribution to the proceedings of the conference "Teleparallel Universes" in Salamanc

Are implants more reliable than severely compromised endodontically treated teeth as abutments for zirconia-based FPDs?

Dissertation im Rahmen einer Publikationspromotion zum Thema: Are implants more reliable than severely compromised endodontically treated teeth as abutments for zirconia-based FPDs?:Inhaltsverzeichnis 1. Ableitung der Rationalen und Einführung in die Thematik 1.1. Ableitung der Rationalen 1.2. Erfolgsprognosen von endodontisch behandelten Zähnen 1.3. Ferrule und dentale Stifte 1.4. Implantate im Frontzahnbereich 1.5. Vergleich endodontisch behandelter Zahn und Implantat 1.6. Anteriore Versorgungen mit festsitzendem Zahnersatz 1.7. Wissenschaftliche Aktualität der Studie 2. Publikation 3. Zusammenfassung der Arbeit 4. Literaturverzeichnis 5. Darstellung und Spezifikation des eigenen wissenschaftlichen Beitrages zur Publikation 6. Erklärung über die eigenständige Abfassung der Arbeit 7. Anlagen 7.1. Abkürzungsverzeichni

Flat connection for rotating vacuum spacetimes in extended teleparallel gravity theories

Teleparallel geometry utilizes Weitzenb\"ock connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi-Civita connection. In extended teleparallel theories, for instance in $f(T)$ or scalar-torsion gravity, the connection must obey its antisymmetric field equations. So far only a few analytic solutions were known. In this note we solve the $f(T,\phi)$ gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation we present the solution also in Boyer-Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities.Comment: minor clarifications and references added; 14 pages, no figures; contributed to the special issue "Selected Papers from Teleparallel Universes in Salamanca 2018

Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes

We discuss the geodesic motion of both massive test particles, following timelike geodesics, and light, following null geodesics, on Finsler spacetimes with cosmological symmetry. Using adapted coordinates on the tangent bundle of the spacetime manifold, we derive the general form of the geodesic equation. Further, we derive a complete set of constants of motion. As an application of these findings, we derive the magnitude-redshift relation for light propagating on a cosmologically symmetric Finsler background, both for a general Finsler spacetime and for particular examples, such as spacetimes equipped with Bogoslovsky and Randers length measures. Our results allow a confrontation of these geometries with observations of the magnitude and redshift of supernovae. © 2017 American Physical Society

Teleparallel axions and cosmology

We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields \emph{teleparallel axions}. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.Comment: 16 page