Geometric transport along circular orbits in stationary axisymmetric spacetimes

Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the zero angular momentum observers and of the Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing "central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.Comment: 33 pages ijmpd latex article with 24 eps figure

Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.Comment: 15 page latex iopart class documen

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.Comment: 9 pages, LaTeX iopart class, no figure

Spacetime Slices and Surfaces of Revolution

Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds physically to the surface gravity $\kappa$ of the black hole horizon. Under conditions that turn out to be closely related, a real surface that possesses rotational symmetry can be equivariantly embedded in 3-dimensional Euclidean space. The embedding does not obviously depend on a parameter. However, the Gaussian curvature is given by a simple formula: If the metric is written $g = \phi(r)^{-1} dr^2 + \phi(r) d\theta^2$, then \K_g=-{1/2}\phi''(r). This note shows that metrics $g$ and $\hat{g}$ occur in dual pairs, and that the embeddings described above are orthogonal facets of a single phenomenon. In particular, the metrics and their respective embeddings differ by a Wick rotation that preserves the ambient symmetry. Consequently, the embedding of $g$ depends on a real parameter. The ambient space is not smooth, and $\kappa$ is inversely proportional to the cone angle at the axis of rotation. Further, the Gaussian curvature of $\hat{g}$ is given by a simple formula that seems not to be widely known.Comment: 15 pages, added reference

Electrocardiogram of the Mixmaster Universe

The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index $\mathcal{S}$, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except for the time used to parametrize it. Its graph versus time characterized by correlated isolated pulses in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such pulse pair arising from a single circuit or ``complex pulse'' around the origin in the complex plane. These pulses in the speciality index and their limiting points on the real axis seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role as a gauge invariant lens through which to view current investigations of inhomogeneous Mixmaster dynamics.Comment: version 3: 20 pages iopart style, 19 eps figure files for 8 latex figures; added example of a transient true spike to contrast with the permanent true spike example from the Lim family of true spike solutions; remarks in introduction and conclusion adjusted and toned down; minor adjustments to the remaining tex

Wearable activity sensors and early pain after total joint arthroplasty.

A prospective observational cohort of 20 primary total hip arthroplasty (n = 12) and total knee arthroplasty (n = 8) patients (mean age: 63 ± 6 years) was passively monitored with a consumer-level wearable activity sensor before and 6 weeks after surgery. Patients were clustered by minimal change or decreased activity using sensor data. Decreased postoperative activity was associated with greater pain reduction (-5.5 vs -2.0, P = .03). All patients surpassed minimal clinical benefit thresholds of total joint arthroplasty (TJA) (Hip Disability and Osteoarthritis Score Junior 30.5 vs 20.8, P = .23; Knee Injury and Osteoarthritis Outcome Score Junior 23.3 vs 18.2, P = .77) within 6 weeks. Patients who objectively "take it easy" after TJA may experience less pain with no difference in early subjective outcome. Remote, passive analysis of outpatient wearable sensor data may permit real-time detection of early problems after TJA

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.Comment: 12 pages LaTeX iopart style, uses PicTex for 1 Figur

The general relativistic Poynting-Robertson effect

The general relativistic version is developed for Robertson's discussion of the Poynting-Robertson effect that he based on special relativity and Newtonian gravity for point radiation sources like stars. The general relativistic model uses a test radiation field of photons in outward radial motion with zero angular momentum in the equatorial plane of the exterior Schwarzschild or Kerr spacetime.Comment: 19 pages iop style, 8 eps figure files for 5 figure

Loop variables in the geometry of a rotating black string

In this paper we analyze in the Wilson loop context the parallel transport of vectors and spinors around a closed loop in the background space-time of a rotating black string in order to classify its global properties. We also examine particular closed orbits in this space-time and verify the Mandelstam relations.Comment: 14 pages, iopart styl