arXiv subjects

Sven Zschocke

Publications and source records attributed to Sven Zschocke.

At least 19 recordsLinked to original sources

arXiv2026

Light deflection in the gravitational field of a solar system body with finite distance of source and observer for sub-micro-arcsecond astrometry

The effect of deflection of a light signal that propagates through the gravitational field of a solar system body at rest is considered in the case that the source and the observer are at a finite distance from the body. The observer is assumed to be located somewhere nearby the Earth, for instance at Lagrange point L2 of the Sun-Earth system, while the spatial position of the celestial light source is arbitrary. The gravitational fields in the exterior of the bodies are described by the full set of time-dependent mass-multipoles and spin-multipoles of these bodies. So the gravitating bodies can be of arbitrary shape, inner structure and rotational motion. The unit tangent vector of the light trajectory at the position of the observer is determined in the 1PN and 1.5PN approximation of the post-Newtonian (PN) scheme. A simplified expression for the unit tangent vector is obtained, where all terms are neglected that together contribute less than 10 nano-arcseconds in light deflection for all astrometric configurations between source, body and observer. It is shown that in the case of an axi-symmetric body the unit tangent vector of the light ray as well as the light deflection are given in terms of Chebyshev polynomials. This fact allows for determining the effect of light deflection in the gravitational fields of the bodies up to any order of the mass-multipoles and spin-multipoles. It is shown that the total light deflection, that is the angle of light deflection where source and observer are located at infinite spatial distance from the body, represents an upper limit of the effect of light deflection. These investigations are aiming at astrometric measurements on the sub-micro-arcsecond level of accuracy.

gr-qc↗

arXiv2026

Gravitational waves and small-field astrometry

Astrometric observations can, in principle, be used to detect gravitational waves. In this paper we give a practical overview of the gravitational wave effects which can be expected specifically in small-field astrometric data. Particular emphasis is placed on the differential effect between pairs of sources within a finite field of view. We also present several general findings that are not restricted to the small-field case. A detailed theoretical derivation of the general astrometric effect of a plane gravitational wave is provided. Numerical simulations, which underline our theoretical findings, are presented. We find that small-field missions suffer from significant detrimental properties, largely because their relatively small fields only allow the measurement of small differential effects which can be expected to be almost totally absorbed by standard plate calibrations.

gr-qc↗

arXiv2025

Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: The basic transformations

Todays astrometry has reached the micro-arcsecond level in angular measurements of celestial objects. The next generations of astrometric facilities are aiming at the sub-micro-arcsecond scale. Sub-micro-arcsecond astrometry requires a considerable improvement in the theory of light propagation in the curved space-time of the solar system. In particular, it is indispensable to determine light trajectories to the second order of the post-Newtonian scheme, where the monopole and quadrupole structure of some solar system bodies need to be taken into account. In reality, both the light source as well as the observer are located at finite spatial distances from the gravitating body. This fact implies for the need to solve the boundary value problem of light propagation, where the light trajectory is fully determined by the spatial positions of source and observer and its unit direction at past infinity. This problem has been solved in a recent investigation. A practical relativistic model of observational data reduction necessitates the determination of the unit tangent vector along the light trajectory at the spatial position of the observer, which is determined by a sequence of several basic transformations. The determination of this unit tangent vector allows one to calculate the impact of the monopole and quadrupole structure of solar system bodies on light deflection on the sub-micro-arcsecond level, both for stellar light sources as well as for light sources located in the solar system. Numerical values for the magnitude of light deflection caused by the monopole and quadrupole structure of the body are given for grazing light rays at the giant planets. The model GREM is presently used for data reduction of the ESA astrometry mission Gaia. It is shown how the implementation of these basic transformations into GREM would proceed for possible future space astrometry missions.

gr-qc↗

arXiv2025

Light propagation in the 2PN approximation in the monopole and quadrupole field of a body at rest: Boundary value problem

In a recent investigation, the initial value problem of light propagation in the gravitational field of a body at rest with monopole and quadrupole structure has been determined in the second post-Newtonian (2PN) approximation. In reality, the light source as well as the observer are located at finite distances from the solar system bodies. This fact requires solving the boundary value problem of light propagation. In this investigation, the solution of the boundary value problem is deduced from the initial value problem of light propagation in 2PN approximation. These results are a basic requirement for subsequent investigations aiming at ultra-highly precise tests of light deflection and time delay in the solar system.

gr-qc↗

arXiv2024

Time delay in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure

The time delay of a light signal which propagates in the gravitational field of an isolated body is considered. The body can be of arbitrary but time-independent shape and inner structure and can be in uniform rotational motion, while the center of mass of the body is assumed to be at rest. The gravitational field is given in the post-Newtonian scheme and in terms of the full set of mass-multipoles and spin-multipoles of the body. The asymptotic configuration is considered, where source and observer are located at spatial infinity from the massive body. It is found that in this asymptotic limit the higher multipole terms of time delay are related to the higher multipole terms of total light deflection. Furthermore, it is shown that the gauge terms vanish in this asymptotic configuration. In case of an axisymmetric body in uniform rotational motion, the higher multipole terms of time delay can be expressed in terms of Chebyshev polynomials. This fact allows one to determine the upper limits of the time delay for higher multipoles. These upper limits represent a criterion to identify those multipoles which contribute significantly to the time delay for a given accuracy of time measurements. It is found that the first mass-multipoles with $l \le 8$ and the first spin-multipoles with $l \le 3$ are sufficient for an accuracy on the femto-second scale of accuracy in time measurements.

gr-qc↗

arXiv2023

Total light deflection in the gravitational field of solar system bodies

The total light deflection represents a concept, which allows one to decide which multipoles need to be implemented in the light trajectory for a given astrometric accuracy. The fundamental quantity of total light deflection is the tangent vector of the light trajectory at future infinity. It is found that this tangent vector is naturally given by Chebyshev polynomials. It is just this remarkable fact, which allows to determine strict upper limits of total light deflection for each individual multipole of solar system bodies. Special care is taken about the gauge terms. It is found that these gauge terms vanish at spatial infinity. The results are applied to the case of light deflection in the gravitational fields of Jupiter and Saturn.

gr-qc↗

arXiv2023

Total light deflection in the gravitational field of an axisymmetric body at rest with full mass and spin multipole structure

The tangent vector of the light trajectory at future infinity and the angle of total light deflection in the gravitational field of an isolated axisymmetric body at rest with full set of mass-multipoles and spin-multipoles is determined in harmonic coordinates in the 1PN and 1.5PN approximation of the post-Newtonian (PN) scheme. It is found that the evaluation of the tangent vector and of the angle of total light deflection caused by mass-multipoles and spin-multipoles leads directly and in a compelling way to Chebyshev polynomials of first and second kind, respectively. This fact allows to determine the upper limits of the total light deflection, which are strictly valid in the 1PN and 1.5PN approximation. They represent a criterion to identify those multipoles which contribute significantly to the total light deflection for a given astrometric accuracy. These upper limits are used to determine the total light deflection in the gravitational field of the Sun and giant planets of the solar system. It is found that the first few mass-multipoles with l \le 10 and the first few spin-multipoles with l \le 3 are sufficient for an accuracy on the nano-arcsecond level in astrometric angular measurements.

gr-qc↗

arXiv2022

Time delay in the quadrupole field of a body at rest in 2PN approximation

The time delay of a light signal in the quadrupole field of a body at rest is determined in the second post-Newtonian (2PN) approximation in harmonic coordinates. For grazing light rays at Sun, Jupiter, and Saturn the 2PN quadrupole effect in time delay amounts up to 0.004, 0.14, and 0.04 pico-second, respectively. These values are compared with the time delay in the first post-Newtonian (1PN and 1.5PN) approximation, where it turns out that only the first eight mass-multipoles and the spin-dipole of these massive bodies are required for a given goal accuracy of 0.001 pico-second in time-delay measurements in the solar system. In addition, the spin-hexapole of Jupiter is required on that scale of accuracy.

gr-qc↗

arXiv2022

Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem

The light trajectory in the gravitational field of one body at rest with monopole and quadrupole structure is determined in the second post-Newtonian (2PN) approximation. The terms in the geodesic equation for light rays are separated into time-independent tensorial coefficients and four kind of time-dependent scalar functions. Accordingly, the first and second integration of geodesic equation can be reduced in each case to only four kind of scalar master integrals. These integrals can be solved in closed form by recurrence relations. The 2PN terms of monopole and quadrupole contribute less than $1$ nano-arcsecond to the total light deflection. There are, however, enhanced terms in the 2PN light deflection, both in case of monopole and quadrupole. These enhanced 2PN terms are caused by the use of an impact vector which is indispensable for modeling of real astrometric measurements. In case of grazing light rays at Jupiter and Saturn, the enhanced 2PN terms, caused by the quadrupole structure of the body, amount up to 0.95 micro-arcseconds and 0.29 micro-arcseconds, respectively. Thus, the 2PN quadrupole terms are relevant for high-precision astrometry on the sub-micro-arcsecond scale of accuracy.

gr-qc↗

arXiv2020

Post-linear metric of a solar system body

A precise modeling of light trajectories in the solar system on the sub-micro-arcsecond and nano-arcsecond scale of accuracy requires the metric tensor of solar system bodies in post-linear approximation. The Multipolar Post-Minkowskian formalism represents a framework for determining the metric density in the exterior of a compact source of matter, which can be regarded as massive solar system body. The knowledge of the metric density, frequently been called gothic metric, allows to deduce the metric tensor. Some aspects are considered about how to determine the metric density and the metric tensor from the field equations of gravity.

gr-qc↗

arXiv2019

Post-linear metric of a compact source of matter

The Multipolar Post-Minkowskian (MPM) formalism represents an approach for determining the metric density in the exterior of a compact source of matter. In the MPM formalism the metric density is given in harmonic coordinates and in terms of symmetric tracefree (STF) multipoles. In this investigation, the post-linear metric density of this formalism is used in order to determine the post-linear metric tensor in the exterior of a compact source of matter. The metric tensor is given in harmonic coordinates and in terms of STF multipoles. The post-linear metric coefficients are associated with an integration procedure. The integration of these post-linear metric coefficients is performed explicitly for the case of a stationary source, where the first multipoles (monopole and quadrupole) of the source are taken into account. These studies are a requirement for further investigations in the theory of light propagation aiming at highly precise astrometric measurements in the solar system, where the post-linear coefficients of the metric tensor of solar system bodies become relevant.

gr-qc↗

arXiv2018

Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem

In this investigation the boundary value problem of light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. The solution of the boundary value problem comprises a set of altogether three transformations: k -> sigma and sigma -> n and k -> n. Analytical solutions of these transformations are given and the upper limit of each individual term is determined. Based on these results, simplified transformations are obtained by keeping only those terms relevant for the given goal accuracy of 1 nano-arcsecond in light deflection. Like in case of light propagation in the gravitational field of one body at rest, there are so-called enhanced terms which are of second post-Newtonian order but contain one and the same typical large numerical factor. Finally, the impact of enhanced terms beyond 2PN approximation is considered. It is found that enhanced 3PN terms are relevant for astrometry on the level of 1 nano-arcsecond in light deflection, while enhanced 4PN terms are negligible, except for grazing rays at the Sun.

gr-qc↗

arXiv2018

Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem

In this investigation the light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. It is found that the light trajectory depends on the acceleration of the body. Some of these acceleration terms are important in order to get well-defined logarithmic functions with dimensionless arguments, while all the other acceleration terms are negligible on the pico-second level of accuracy in time-delay measurements. The expressions of the observables total light deflection and time delay are determined.

gr-qc↗

arXiv2017

Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation

An analytical solution for the light trajectory in the near-zone of the gravitational field of one pointlike body in arbitrary slow-motion in the post-post-Newtonian approximation is presented in harmonic gauge. Expressions for total light deflection and time delay are given. The presented solution is a further step toward high-precision astrometry aiming at nano-arcsecond level of accuracy.

gr-qc↗

arXiv2017

Light propagation in the gravitational field of N arbitrarily moving bodies in 1PN approximation for high-precision astrometry

The light-trajectory in the gravitational field of N extended bodies in arbitrary motion is determined in the first post-Newtonian approximation. According to the theory of reference systems, the gravitational fields of these massive bodies are expressed in terms of their intrinsic multipoles, allowing for arbitrary shape and inner structure of these bodies. The results of this investigation aim towards a consistent general-relativistic theory of light propagation in the Solar system for high-precision astrometry at sub-micro-arcsecond level of accuracy.

astro-ph.IM↗

arXiv2017

Light propagation in the gravitational field of N arbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry

High-precision astrometry on sub-micro-arcsecond level in angular resolution requires accurate determination of the trajectory of a light-signal from the celestial light source through the gravitational field of the Solar system toward the observer. In this investigation the light trajectory in the gravitational field of N moving bodies is determined in the 1.5 post-Newtonian approximation. In the approach presented two specific issues of particular importance are accounted for: (1) According to the recommendations of International Astronomical Union, the metric of the Solar system is expressed in terms of intrinsic mass-multipoles and intrinsic spin-multipoles of the massive bodies, allowing for arbitrary shape, inner structure and rotational motion of the massive bodies of the Solar system. (2) The Solar system bodies move along arbitrary worldlines which can later be specified by Solar system ephemeris. The presented analytical solution for light trajectory is a primary requirement for extremely high-precision astrometry on sub-micro-arcsecond level of accuracy and associated massive computations in astrometric data reduction. An estimation of the numerical magnitude for time delay and light deflection of the leading multipoles is given.

gr-qc↗

arXiv2015

Differential HBT Method for Binary Stars

Two photon correlations are studied for a binary star system. It is investigated how the differential Hanbury Brown and Twiss (HBT) approach can be used in order to determine orbital parameters of a binary star.

astro-ph.IM↗

arXiv2014

Gravitational field of one uniformly moving extended body and N arbitrarily moving pointlike bodies in post-Minkowskian approximation

High precision astrometry, space missions and certain tests of General Relativity, require the knowledge of the metric tensor of the solar system, or more generally, of a gravitational system of N extended bodies. Presently, the metric of arbitrarily shaped, rotating, oscillating and arbitrarily moving N bodies of finite extension is only known for the case of slowly moving bodies in the post-Newtonian approximation, while the post-Minkowskian metric for arbitrarily moving celestial objects is known only for pointlike bodies with mass-monopoles and spin-dipoles. As one more step towards the aim of a global metric for a system of N arbitrarily shaped and arbitrarily moving massive bodies in post-Minkowskian approximation, two central issues are on the scope of our investigation: (i) We first consider one extended body with full multipole structure in uniform motion in some suitably chosen global reference system. For this problem a co-moving inertial system of coordinates can be introduced where the metric, outside the body, admits an expansion in terms of Damour-Iyer moments. A Poincare transformation then yields the corresponding metric tensor in the global system in post-Minkowskian approximation. (ii) It will be argued why the global metric, exact to post-Minkowskian order, can be obtained by means of an instantaneous Poincare transformation for the case of pointlike mass-monopoles and spin-dipoles in arbitrary motion.

astro-ph.IM↗