arXiv subjects

D. Vogt

Publications and source records attributed to D. Vogt.

17 recordsLinked to original sources

arXiv2014

Relativistic ring models

Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with one ring, two rings and a disc with a ring. Also, the circular velocity of a test particle and its stability when performing circular orbits are presented in all these models. In general, we find that regions of non-stability appear between the rings when they become thinner.

gr-qc↗

arXiv2010

Potential-density pairs for bent bars

A method is presented to bend a thin massive line when the curvature is small. The procedure is applied to a homogeneous thin bar with two types of curvatures. One of them mimics a galactic bar with two spiral arms at its tips. It is showed that if the bending function is a linear combination of Legendre polynomials, then the bent potential is an exact solution of the Laplace equation. A transformation is applied on the thin bent bars to generate three-dimensional potential-density pairs without singularities. The potentials of the thin bent bars are also used to generate non-axisymmetric planar distributions of matter.

astro-ph.GA↗

arXiv2010

Analytical potential-density pairs for bars

An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally thin bars with a given linear density profile. By means of a suitable transformation, softened bars that are free of singularities are also obtained. As an application we study the equilibrium points and stability for the motion of test particles in the gravitational field for three models of rotating bars.

astro-ph.GA↗

arXiv2010

Newtonian and General Relativistic Models of Spherical Shells - II

A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by inversion transformations of spheres and of the finite shells. We also present a family of double shells with finite thickness. All potential-density pairs are analytical and can be stated in terms of elementary functions. For the above-mentioned structures, we study the circular orbits of test particles and their stability with respect to radial perturbations. All examples presented are found to be stable. A particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian families of spheres and shells. The matter of these structures is anisotropic, and the degree of anisotropy is a function of the radius.

gr-qc↗

arXiv2009

Newtonian and General Relativistic Models of Spherical Shells

A family of spherical shells with varying thickness is derived by using a simple Newtonian potential-density pair. Then, a particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian family of shells. The matter of these relativistic shells presents equal azimuthal and polar pressures, while the radial pressure is a constant times the tangential pressure. We also make a first study of stability of both the Newtonian and relativistic families of shells.

gr-qc↗

arXiv2009

Analytical potential-density pairs from complex-shifted Kuzmin-Toomre discs

The complex-shift method is applied to the Kuzmin-Toomre family of discs to generate a family of non-axisymmetric flat distributions of matter. These are then superposed to construct non-axisymmetric flat rings. We also consider triaxial potential-density pairs obtained from these non-axisymmetric flat systems by means of suitable transformations. The use of the imaginary part of complex-shifted potential-density pairs is also discussed.

astro-ph.GA↗

arXiv2009

Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

The Kuzmin-Toomre family of discs is used to construct potential-density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular orbits are calculated for these structures. A few examples of three-dimensional potential-density pairs of "inflated" flat rings (toroidal mass distributions) are presented.

astro-ph.GA↗

arXiv2008

Exact General Relativistic Discs and the Advance of Perihelion

The advance of perihelion for geodesic motion on the galactic plane of some exact general relativistic disc solutions is calculated. Approximate analytical and numerical results are presented for the static Chazy-Curzon and the Schwarzschild discs in Weyl coordinates, the Schwarzschid disc in isotropic coordinantes and the stationary Kerr disc in the Weyl-Lewis-Papapetrou metrics. It is found that for these disc models the advance of perihelion may be an increasing or decreasing function of the orbital excentricity. The precession due to Newtonian gravity for these disc models is also calculated.

astro-ph↗

arXiv2006

Exact General Relativistic Rotating Disks Immersed in Rotating Dust Generated from van Stockum Solutions

A class of exact general relativistic rotating thick disks surrounded by rotating dust is constructed by applying the ``displace, cut, fill and reflect'' method on the van Stockum class of metrics. Two particular solutions are considered in detail. We find that the disks have annular regions with negative energy density and heat flow is present in most of the radial extension of the disk. It is shown that thin disks are composed of exotic matter with an equation of state of cosmic strings or struts. We also comment the recent relativistic galactic model proposed by Cooperstock and Tieu and the presence of an additional disk of exotic matter in their model.

astro-ph↗

arXiv2006

On Multipolar Analytical Potentials for Galaxies

We present analytical potential-density pairs in three dimensions for the gravitational field of galaxies, obtained by thickening the multipolar expansion up to the quadrupole term. These may be interpreted as generalizations of the Miyamoto and Nagai potential-density pairs. With a suitable restriction on the possible values of the multipole moments, the density distributions are positive and monotone decreasing functions of the radial and axial coordinates.

astro-ph↗

arXiv2005

Comments on "Perspectives on Galactic Dynamics via General Relativity"

In this comment we question some arguments presented in astro-ph/0512048 to refuse the presence of an singular mass surface layer. In particular, incorrect expressions are used for the disk's surface mass density. We also point out that the procedure of removing the descontinuity on the $z=0$ plane with a region of continuous density gradient generates other two regions of descontinuities with singular mass surface layers making the model unrealistic.

astro-ph↗

arXiv2005

Presence of exotic matter in the Cooperstock and Tieu galaxy model

We analyze the presence of an additional singular thin disk in the recent General Relativistic model of galactic gravitational field proposed by Cooperstock and Tieu. The physical variables of the disk's energy-momentum tensor are calculated. We show that the disk is made of exotic matter, either cosmic strings or struts with negative energy density.

astro-ph↗

arXiv2005

Relativistic Models of Galaxies

A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model three-dimensional distributions of matter in galaxies. The components of the energy-momentum tensor are calculated for the first two Miyamoto-Nagai potentials and a particular potential due to Satoh. The three potentials yield distributions of matter in which all tensions are pressures and all energy conditions are satisfied for certain ranges of the free parameters. A few non-planar geodesic orbits are computed for one of the potentials and compared with the Newtonian case. Rotation is also incorporated to the models and the effects of the source rotation on the rotation profile are calculated as first order corrections by using an approximate form of the Kerr metric in isotropic coordinates.

astro-ph↗

arXiv2005

New Models of General Relativistic Static Thick Disks

New families of exact general relativistic thick disks are constructed using the ``displace, cut, fill and reflect'' method. A class of functions used to ``fill'' the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the function's curvature further restrict the ranges of the free parameters that allow phisically acceptable disks. Then this class of functions together with the Schwarzschild metric is employed to construct thick disks in isotropic, Weyl and Schwarzschild canonical coordinates. In these last coordinates an additional function must be added to one of the metric coefficients to generate exact disks. Disks in isotropic and Weyl coordinates satisfy all energy conditions, but those in Schwarzschild canonical coordinates do not satisfy the dominant energy condition.

gr-qc↗

arXiv2004

Exact Relativistic Static Charged Perfect Fluid Disks

Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static charged disks made of perfect fluid based on the Reissner-Nordström solution in isotropic coordinates. We also derive a simple stability condition for charged and non charged perfect fluid disks. As expected, we find that the presence of charge increases the regions of instability of the disks.

gr-qc↗

arXiv2004

A General Relativistic Model for the Gravitational Field of Active Galactic Nuclei Surrounded by a Disk

An exact but simple general relativistic model for the gravitational field of active galactic nuclei is constructed, based on the superposition in Weyl coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent matter jets. The influence of the rods on the matter properties of the disk and on its stability is examined. We find that in general they contribute to destabilize the disk. Also the oscillation frequencies for perturbed circular geodesics on the disk are computed, and some geodesic orbits for the superposed metric are numerically calculated.

gr-qc↗

arXiv2003

On the Solutions of the Lorentz-Dirac Equation

We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic example of the non-relativistic harmonic oscillator with radiation reaction. We also illustrate removal of the noncasual pre-acceleration with the introduction of a small correction in the Lorentz-Dirac equation.

physics.class-ph↗