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Robert T. Jantzen

Publications and source records attributed to Robert T. Jantzen.

46 records · Page 3Linked to original sources
arXiv2003

Gravitomagnetism in the Kerr-Newman-Taub-NUT spacetime

We study the motion of test particles and electromagnetic waves in the Kerr-Newman-Taub-NUT spacetime in order to elucidate some of the effects associated with the gravitomagnetic monopole moment of the source. In particular, we determine in the linear approximation the contribution of this monopole to the gravitational time delay and the rotation of the plane of the polarization of electromagnetic waves. Moreover, we consider "spherical" orbits of uncharged test particles in the Kerr-Taub-NUT spacetime and discuss the modification of the Wilkins orbits due to the presence of the gravitomagnetic monopole.

gr-qc↗
arXiv2003

Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still Going Around in Circles After All These Years

The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these frames can be explicitly constructed using a Killing-Yano tensor as shown by Marck. For accelerated or geodesic circular orbits in such spacetimes, both parallel and Fermi-Walker transported frames can be given, and allow one to study circular holonomy and related clock and spin transport effects. In particular the total angle of rotation that a spin vector undergoes around a closed loop can be expressed in a factored form, where each factor is due to a different relativistic effect, in contrast with the usual sum of terms decomposition. Finally the Thomas precession frequency is shown to be a special case of the simple relationship between the parallel transport and Fermi-Walker transport frequencies for stationary circular orbits.

gr-qc↗
arXiv2002

Circular holonomy in the Taub-NUT spacetime

Parallel transport around closed circular orbits in the equatorial plane of the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic monopole parameter on circular holonomy transformations. Investigating the boost/rotation decomposition of the connection 1-form matrix evaluated along these orbits, one finds a situation that reflects the behavior of the general orthogonally transitive stationary axisymmetric case and indeed along Killing trajectories in general.

gr-qc↗
arXiv2001

Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes

Stationary axisymmetric spacetimes containing a pair of oppositely-rotating periodically-intersecting circular geodesics allow the study of various so-called `clock effects' by comparing either observer or geodesic proper time periods of orbital circuits defined by the observer or the geodesic crossing points. This can be extended from a comparison of clocks to a comparison of parallel transported vectors, leading to the study of special elements of the spacetime holonomy group. The band of holonomy invariance found for a dense subset of special geodesic orbits outside a certain radius in the static case does not exist in the nonstatic case. In the Kerr spacetime the dimensionless frequencies associated with parallel transport rotations can be expressed as ratios of the proper and average coordinate periods of the circular geodesics.

gr-qc↗
arXiv2001

The Many Faces of Gravitoelectromagnetism

The numerous ways of introducing spatial gravitational forces are fit together in a single framework enabling their interrelationships to be clarified. This framework is then used to treat the ``acceleration equals force" equation and gyroscope precession, both of which are then discussed in the post-Newtonian approximation, followed by a brief examination of the Einstein equations themselves in that approximation.

gr-qc↗
arXiv2001

Gravitoelectromagnetism: Just a Big Word?

Arguments are made in favor of broadening the scope of the various approaches to splitting spacetime into a single common framework in which measured quantities, derivative operations, and adapted coordinate systems are clearly understood in terms of associated test observer families. This ``relativity of splitting formalisms" for fully nonlinear gravitational theory has been tagged with the name "gravitoelectromagnetism" because of the well known analogy between its linearization and electromagnetism, and it allows relationships between the various approaches to be better understood and makes it easier to extrapolate familiarity with one approach to the others. This is important since particular problems or particular features of those problems in gravitational theory are better suited to different approaches, and the present barriers between the proponents of each individual approach sometimes prevent the best match from occurring.

gr-qc↗
arXiv2001

Spatially Homogeneous Dynamics: A Unified Picture

The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial homogeneity. A parameter-dependent decomposition of the metric variables adapted to the symmetry breaking effects of the nonabelian Bianchi types on the "free dynamics" leads to a reduction of the equations of motion for those variables to a 2-dimensional time-dependent Hamiltonian system containing various time-dependent potentials which are explicitly described and diagrammed. These potentials are extremely useful in deducing the gross features of the evolution of the metric variables.

gr-qc↗
arXiv2001

Gravitomagnetism and Relative Observer Clock Effects

The gravitomagnetic clock effect and the Sagnac effect for circularly rotating orbits in stationary axisymmetric spacetimes are studied from a relative observer point of view, clarifying their relationships and the roles played by special observer families. In particular Semerák's recent characterization of extremely accelerated observers in terms of the two-clock clock effect is shown to be complemented by a similarly special property of the single-clock clock effect.

gr-qc↗
arXiv1995

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.

gr-qc↗