arXiv subjects

Dirk Puetzfeld

Publications and source records attributed to Dirk Puetzfeld.

At least 55 records · Page 3Linked to original sources

arXiv2013

Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling

We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of 9 parity-even curvature invariants. The equations of motion for spinning test bodies in such theories are explicitly derived by means of Synge's expansion technique. Our findings generalize previous results in the literature and allow for a direct comparison to the general relativistic equations of motion of pole-dipole test bodies.

gr-qc↗

arXiv2013

Influence of internal structure on the motion of test bodies in extreme mass ratio situations (MG13)

We present some recent results on the motion of test bodies with internal structure in General Relativity. On the basis of a multipolar approximation scheme, we study the motion of extended test bodies endowed with an explicit model for the quadrupole. The model is inspired by effective actions recently proposed in the context of the post-Newtonian approximation, including spin-squared and tidal contributions. In the equatorial plane of the Kerr geometry, the motion can be characterized by an effective potential of the binding energy. We compare our findings to recent results for the conservative part of the self-force in astrophysically realistic situations.

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arXiv2012

Spinning particles in de Sitter spacetime

We report on the multipolar equations of motion for spinning test bodies in the de Sitter spacetime of constant positive curvature. The dynamics of spinning particles is discussed for the two supplementary conditions of Frenkel and Tulczyjew. Furthermore, the 4-momentum and the spin are explicitly expressed in terms of the spacetime coordinates with the help of the 10 Killing vectors available in de Sitter spacetime.

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arXiv2011

Dynamics of test bodies with spin in de Sitter spacetime

We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.

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arXiv2010

Multipolar equations of motion for extended test bodies in General Relativity

We derive the equations of motion of an extended test body in the context of Einstein's theory of gravitation. The equations of motion are obtained via a multipolar approximation method and are given up to the quadrupolar order. Special emphasis is put on the explicit construction of the so-called canonical form of the energy-momentum density. The set of gravitational multipolar moments and the corresponding equations of motion allow for a systematic comparison to competing multipolar approximation schemes.

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arXiv2009

The motion of test bodies with microstructure in gauge gravity models

We report on the explicit form of the equations of motion of pole-dipole particles for a very large class of gravitational theories. The non-Riemannian framework in which the equations are derived allows for a unified description of nearly all known gravitational theories. The propagation equations are obtained with the help of a multipole expansion method from the conservation laws that follow from Noether's theorem. The well-known propagation equations of general relativity, e.g., as given by Mathisson and Papapetrou, represent a special case in our general framework. Our formalism allows for a direct identification of the couplings between the matter currents and the gravitational field strengths in gauge gravity models. In particular, it illustrates the need for matter with microstructure for the detection of non-Riemannian spacetime geometries.

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arXiv2009

Probing non-Riemannian spacetime geometry

The equations of motion for matter in non-Riemannian spacetimes are derived via a multipole method. It is found that only test bodies with microstructure couple to the non-Riemannian spacetime geometry. Consequently it is impossible to detect spacetime torsion with the satellite experiment Gravity Probe B, contrary to some recent claims in the literature.

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arXiv2009

Propagation equations for deformable test bodies with microstructure in extended theories of gravity

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.

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arXiv2008

Motion of test bodies in theories with nonminimal coupling

We derive the equations of motion of test bodies for a theory with nonminimal coupling by means of a multipole method. The propagation equations for pole-dipole particles are worked out for a gravity theory with a very general coupling between the curvature scalar and the matter fields. Our results allow for a systematic comparison with the equations of motion of general relativity and other gravity theories.

astro-ph↗

arXiv2006

PROCRUSTES: A computer algebra package for post-Newtonian calculations in General Relativity

We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the post-Newtonian approximation. The package structure is modular and allows for an easy modification by the user. The set of routines can be used to verify hand calculations or to generate the input for further numerical investigations.

gr-qc↗

arXiv2005

Beyond linearized cosmology

We comment on the necessity of a unified approximative scheme within relativistic cosmology which would allow us to classify different cosmological models in a systematic way. We also report on recent progresses in formulating a cosmological post-Newtonian approximation and the problems related to such a scheme.

astro-ph↗

arXiv2005

Cosmological nonlinear hydrodynamics with post-Newtonian corrections

The post-Newtonian (PN) approximation, based on the assumptions of weak gravitational fields and slow motions, provides a way to estimate general relativistic effects in the fully nonlinear evolution stage of the large-scale cosmic structures. We extend Chandrasekhar's first order PN (1PN) hydrodynamics based on the Minkowski background to the Robertson-Walker background. We assume the presence of Friedmann's cosmological spacetime as a background. In the background we include the three-space curvature, the cosmological constant and general pressure. In the Newtonian order and 1PN order we include general pressure, stress, and flux. The Newtonian hydrodynamic equations appear naturally in the 0PN order. The spatial gauge degree of freedom is fixed in a unique manner and the basic equations are arranged without taking the temporal gauge condition. In this way we can conveniently try alternative temporal gauge conditions. We investigate a number of temporal gauge conditions under which all the remaining variables are equivalently gauge-invariant. Our aim is to present the fully nonlinear 1PN equations in a form suitable for implementation in conventional Newtonian hydrodynamic simulations with minimal extensions. The 1PN terms can be considered as relativistic corrections added to the well known Newtonian equations. The proper arrangement of the variables and equations in combination with suitable gauge conditions would allow the possible future 1PN cosmological simulations to become more tractable. Our equations and gauges are arranged for that purpose. We suggest ways of controlling the numerical accuracy. The typical 1PN order terms are about $10^{-6} \sim 10^{-4}$ times smaller than the Newtonian terms.

astro-ph↗

arXiv2005

Prospects of Non-Riemannian Cosmology

In this work we provide the motivation for considering non-Riemannian models in cosmology. Non-Riemannian extensions of general relativity theory have been studied for a long time. In such theories the spacetime continuum is no longer described by the metric alone but endowed with additional geometric quantities. These new quantities can be coupled to the intrinsic properties of matter in a very natural way and therefore provide a richer gravitational theory, which might be necessary in view of the recent cosmological evidence for dark matter and dark energy. In this work we mainly focus on the concepts in metric-affine gravity and point out their possible significance in the process of cosmological model building.

astro-ph↗

arXiv2004

Complementary constraints from FR IIb radio galaxies and X-ray gas mass fractions in clusters on non-standard cosmological models

We use recent measurements of the dimensionless coordinate distances from Fanaroff-Riley Type IIb radio galaxies and the X-ray gas mass fractions in clusters to constrain the parameters of a non-standard cosmological model. This work complements our recent analysis of the SN Ia data within a non-Riemannian cosmological model. We use two independent data sets to constrain the new density parameter $Ω_ψ$, which is related to the non-Riemannian structure of the underlying spacetime and supplements the field equations that are very similar to the usual Friedmann equations of general relativity. Thereby we place an upper limit on the presence of non-Riemannian quantities in the late stages of the universe. The numerical results of this work also apply to several anisotropic cosmological models which, on the level of the field equations, exhibit a similar scaling behavior of the density parameters like our non-Riemannian model.

astro-ph↗

arXiv2004

Status of non-Riemannian cosmology

We provide a brief chronological guide to the literature on non-Riemannian cosmological models. Developments in this field are traced back to the early seventies and are given in table form.

gr-qc↗

arXiv2004

Testing non-standard cosmological models with supernovae

In this work we study the magnitude-redshift relation of a non-standard cosmological model. The model under consideration was firstly investigated within a special case of metric-affine gravity (MAG) and was recently recovered via different approaches by two other groups. Apart from the usual cosmological parameters for pressure-less matter $Ω_{\rm m}$, cosmological constant/dark energy $Ω_λ$, and radiation $Ω_{\rm r}$ a new density parameter $Ω_ψ$ emerges. The field equations of the model reduce to a system which is effectively given by the usual Friedmann equations of general relativity, supplied by a correction to the energy density and pressure in form of $Ω_ψ$, which is related to the non-Riemannian structure of the underlying spacetime. We search for the best-fit parameters by using recent SN Ia data sets and constrain the possible contribution of a new dark-energy like component at low redshifts, thereby we put an upper limit on the presence of non-Riemannian quantities in the late stages of the universe. In addition the impact of placing the data in redshift bins of variable size is studied. The numerical results of this work also apply to several anisotropic cosmological models which, on the level of the field equations, exhibit a similar scaling behavior of the density parameters like our non-Riemannian model.

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arXiv2002

A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions

In this first article of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion $T^α$ and nonmetricity $Q_{αβ}$, are proportional to the Weyl 1-form. The hypermomentum $Δ_{αβ}$ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).

gr-qc↗

arXiv2002

A cosmological model in Weyl-Cartan spacetime: II. Magnitude-redshift relation

In this second part of our series of articles on alternative cosmological models we investigate the observational consequences for the new Weyl-Cartan model proposed earlier. We review the derivation of the magnitude-redshift relation within the standard FLRW model and characterize its dependence on the underlying cosmological model. With this knowledge at hand we derive the magnitude-redshift relation within our new Weyl-Cartan model. We search for the best-fit parameters by using the combined data set of 92 SNe of type Ia as compiled by Wang, which is based on recent supernova data of Perlmutter et al. and Riess et al. Additionally, we compare our best-fit parameters with the results of several other groups which performed similar analysis within the standard cosmological model as well as in non-standard models.

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