Consistent modeling of the geodetic precession in Earth rotation

A highly precise model for the motion of a rigid Earth is indispensable to reveal the effects of non-rigidity in the rotation of the Earth from observations. To meet the accuracy goal of modern theories of Earth rotation of 1 microarcsecond (muas) it is clear, that for such a model also relativistic effects have to be taken into account. The largest of these effects is the so called geodetic precession. In this paper we will describe this effect and the standard procedure to deal with it in modeling Earth rotation up to now. With our relativistic model of Earth rotation Klioner et al. (2001) we are able to give a consistent post-Newtonian treatment of the rotational motion of a rigid Earth in the framework of General Relativity. Using this model we show that the currently applied standard treatment of geodetic precession is not correct. The inconsistency of the standard treatment leads to errors in all modern theories of Earth rotation with a magnitude of up to 200 muas for a time span of one century.Comment: 6 pages, 4 figures, 1 table, published in the Proceedings of the VII Hotine-Marussi Symposium, Chapter 4

A note on the computation of geometrically defined relative velocities

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intrinsic expressions for Fermi and astrometric relative velocities avoiding terms that involve the evolution of the relative position of the test particle. For this purpose, the proofs given in this paper can serve as inspiration.Comment: 8 pages, 2 figure

Units of relativistic time scales and associated quantities

This note suggests nomenclature for dealing with the units of various astronomical quantities that are used with the relativistic time scales TT, TDB, TCB and TCG. It is suggested to avoid wordings like "TDB units" and "TT units" and avoid contrasting them to "SI units". The quantities intended for use with TCG, TCB, TT or TDB should be called "TCG-compatible", "TCB-compatible", "TT-compatible" or "TDB-compatible", respectively. The names of the units second and meter for numerical values of all these quantities should be used with out any adjectives. This suggestion comes from a special discussion forum created within IAU Commission 52 "Relativity in Fundamental Astronomy"

Comment on superluminality in general relativity

General relativity provides an appropriate framework for addressing the issue of sub- or superluminality as an apparent effect. Even though a massless particle travels on the light cone, its average velocity over a finite path measured by different observers is not necessarily equal to the velocity of light, as a consequence of the time dilation or contraction in gravitational fields. This phenomenon occurs in either direction (increase or depletion) irrespectively of the details and strength of the gravitational interaction. Hence, it does not intrinsically guarantee superluminality, even when the gravitational field is reinforced.Comment: 6 page

Dynamical constraints on some orbital and physical properties of the WD0137-349 A/B binary system

In this paper I deal with the WD0137-349 binary system consisting of a white dwarf (WD) and a brown dwarf (BD) in a close circular orbit of about 116 min. I, first, constrain the admissible range of values for the inclination i by noting that, from looking for deviations from the third Kepler law, the quadrupole mass moment Q would assume unlikely large values, incompatible with zero at more than 1-sigma level for i 43 deg. Then, by conservatively assuming that the most likely values for i are those that prevent such an anomalous behavior of Q, i.e. those for which the third Kepler law is an adequate modeling of the orbital period, I obtain i=39 +/- 2 deg. Such a result is incompatible with the value i=35 deg quoted in literature by more than 2 sigma. Conversely, it is shown that the white dwarf's mass range obtained from spectroscopic measurements is compatible with my experimental range, but not for i=35 deg. As a consequence, my estimate of $i$ yields an orbital separation of a=(0.59 +/- 0.05)R_Sun and an equilibrium temperature of BD of T_eq=(2087 +/- 154)K which differ by 10% and 4%, respectively, from the corresponding values for i=35 deg.Comment: LaTex2e, 11 pages, 3 figures, no tables. It refers to gr-qc/0611126 and better clarify the result obtained there. Accepted by Astrophysics and Space Scienc

The gravitational analogue to the hydrogen atom (A summer study at the borders of quantum mechanics and general relativity)

This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The aim of the project was to study the Dirac equation in curved space time. To obtain the general relativistic Dirac equation we use the formulation of gravity as a gauge theory in the first part. After these general considerations we restrict the further discussion to the special case of the Schwarzschild metric. This setting corresponds to the hydrogen atom, with the electromagnetic field replaced by gravity. Although there is a singularity at the event horizon it turns out that a regular solution of the time independent Dirac equation exists. Finally the Dirac equation is solved numerically using suitable boundary conditions.Comment: 19 pages, 3 figure