arXiv subjects

Robert J. van den Hoogen

Publications and source records attributed to Robert J. van den Hoogen.

5 recordsLinked to original sources

arXiv2024

Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames

We present the proper co-frame and its corresponding (diagonal) co-frame/spin connection pair for spherically symmetric geometries which can be used as an initial ansatz in any theory of teleparallel gravity. The Lorentz transformation facilitating the move from one co-frame to the other is also presented in factored form. The factored form also illustrates the nature of the two degrees of freedom found in the spin connection. The choice of coordinates in restricting the number of arbitrary functions is also presented. Beginning with a thorough presentation of teleparallel gravity using the metric affine gauge theory approach and concentrating on f(T) teleparallel gravity, we express the field equations in the diagonal co-frame. We argue that the choice of diagonal co-frame may be more advantageous over the proper co-frame choice. Finally, assuming one additional symmetry, we restrict ourselves to the Kantowski-Sachs tele-parallel geometries, and determine some solutions.

gr-qc↗

arXiv2024

Symmetries in Riemann-Cartan Geometries

Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many important differences when compared to Riemannian geometries. One notable difference, is the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries.

gr-qc↗

arXiv2023

Generalized Teleparallel de Sitter geometries

Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin connection. The appropriate notion of a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the importance of the de Sitter geometry and Einstein spaces within general relativity, we shall describe teleparallel de Sitter geometries and discuss their possible generalizations. In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.

gr-qc↗

arXiv2023

Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame

A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation scheme can be transformed to one in which perturbations all take place within the co-frame. A covariant definition of a teleparallel Minkowski geometry is proposed. We compute the perturbed field equations for $f(T)$ teleparallel gravity and discuss the stability of the teleparallel Minkowski geometry within $f(T)$ teleparallel gravity.

gr-qc↗

arXiv1999

Scaling Solutions in Robertson-Walker Spacetimes

We investigate the stability of cosmological scaling solutions describing a barotropic fluid with $p=(γ-1)ρ$ and a non-interacting scalar field $ϕ$ with an exponential potential $V(ϕ)=V_0\e^{-κϕ}$. We study homogeneous and isotropic spacetimes with non-zero spatial curvature and find three possible asymptotic future attractors in an ever-expanding universe. One is the zero-curvature power-law inflation solution where $Ω_ϕ=1$ ($γ<2/3,κ^2<3γ$ and $γ>2/3,κ^2<2$). Another is the zero-curvature scaling solution, first identified by Wetterich, where the energy density of the scalar field is proportional to that of matter with $Ω_ϕ=3γ/κ^2$ ($γ<2/3,κ^2>3γ$). We find that this matter scaling solution is unstable to curvature perturbations for $γ>2/3$. The third possible future asymptotic attractor is a solution with negative spatial curvature where the scalar field energy density remains proportional to the curvature with $Ω_ϕ=2/κ^2$ ($γ>2/3,κ^2>2$). We find that solutions with $Ω_ϕ=0$ are never late-time attractors.

gr-qc↗