Spinning test particles and clock effect in Kerr spacetime

We study the motion of spinning test particles in Kerr spacetime using the Mathisson-Papapetrou equations; we impose different supplementary conditions among the well known Corinaldesi-Papapetrou, Pirani and Tulczyjew's and analyze their physical implications in order to decide which is the most natural to use. We find that if the particle's center of mass world line, namely the one chosen for the multipole reduction, is a spatially circular orbit (sustained by the tidal forces due to the spin) then the generalized momentum $P$ of the test particle is also tangent to a spatially circular orbit intersecting the center of mass line at a point. There exists one such orbit for each point of the center of mass line where they intersect; although fictitious, these orbits are essential to define the properties of the spinning particle along its physical motion. In the small spin limit, the particle's orbit is almost a geodesic and the difference of its angular velocity with respect to the geodesic value can be of arbitrary sign, corresponding to the spin-up and spin-down possible alignment along the z-axis. We also find that the choice of the supplementary conditions leads to clock effects of substantially different magnitude. In fact, for co-rotating and counter-rotating particles having the same spin magnitude and orientation, the gravitomagnetic clock effect induced by the background metric can be magnified or inhibited and even suppressed by the contribution of the individual particle's spin. Quite surprisingly this contribution can be itself made vanishing leading to a clock effect undistiguishable from that of non spinning particles. The results of our analysis can be observationally tested.Comment: IOP macros, eps figures n. 12, to appear on Classical and Quantum Gravity, 200

Spinning test particles and clock effect in Schwarzschild spacetime

We study the behaviour of spinning test particles in the Schwarzschild spacetime. Using Mathisson-Papapetrou equations of motion we confine our attention to spatially circular orbits and search for observable effects which could eventually discriminate among the standard supplementary conditions namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the world line chosen for the multipole reduction and whose unit tangent we denote as $U$ is a circular orbit then also the generalized momentum $P$ of the spinning test particle is tangent to a circular orbit even though $P$ and $U$ are not parallel four-vectors. These orbits are shown to exist because the spin induced tidal forces provide the required acceleration no matter what supplementary condition we select. Of course, in the limit of a small spin the particle's orbit is close of being a circular geodesic and the (small) deviation of the angular velocities from the geodesic values can be of an arbitrary sign, corresponding to the possible spin-up and spin-down alignment to the z-axis. When two spinning particles orbit around a gravitating source in opposite directions, they make one loop with respect to a given static observer with different arrival times. This difference is termed clock effect. We find that a nonzero gravitomagnetic clock effect appears for oppositely orbiting both spin-up or spin-down particles even in the Schwarzschild spacetime. This allows us to establish a formal analogy with the case of (spin-less) geodesics on the equatorial plane of the Kerr spacetime. This result can be verified experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum gravity, 200

Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters $M$ (mass), $Q$ (charge), $a$ (rotation) and $L$ (NUT). We then, calculate the total exterior energy using the energy-momentum complex given by M{\o}ller in the framework of Weitzenb$\ddot{o}$ck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only non-vanishing components of the angular momentum is in the Z direction.Comment: Latex. Will appear in IJMP

Equivalent Mid-Term Results of Open vs Endoscopic Gluteal Tendon Tear Repair Using Suture Anchors in Forty-Five Patients.

BackgroundLittle is known about the relative efficacy of open (OGR) vs endoscopic (EGR) gluteal tendon repair of gluteal tendon tears in minimizing pain and restoring function. Our aim is to compare these 2 surgical techniques and quantify their impact on clinical outcomes.MethodsAll patients undergoing gluteal tendon tear repair at our institution between 2015 and 2018 were retrospectively reviewed. Pain scores, limp, hip abduction strength, and the use of analgesics were recorded preoperatively and at last follow-up. The Hip disability and Osteoarthritis Outcome Score Junior and Harris Hip Score Section1 were obtained at last follow-up. Fatty degeneration was quantified using the Goutallier-Fuchs Classification (GFC). Statistical analysis was conducted using one-way analysis of variance and t-tests.ResultsForty-five patients (mean age 66, 87% females) met inclusion criteria. Average follow-up was 20.3 months. None of the 10 patients (22%) undergoing EGR had prior surgery. Of 35 patients (78%) undergoing OGR, 12 (27%) had prior hip replacement (75% via lateral approach). The OGRs had more patients with GFC ≥2 (50% vs 11%, P = .02) and used more anchors (P = .03). Both groups showed statistical improvement (P ≤ .01) for all outcomes measured. GFC >2 was independently associated with a worst limp and Harris Hip Score Section 1 score (P = .05). EGR had a statistically higher opioid use reduction (P < .05) than OGR. Other comparisons between EGR and OGR did not reach statistical significance.ConclusionIn this series, open vs endoscopic operative approach did not impact clinical outcomes. More complex tears were treated open and with more anchors. Fatty degeneration adversely impacted outcomes. Although further evaluation of the efficacy of EGR in complex tears is indicated, both approaches can be used successfully

Designing Bandwidth-Efficient Stabilizing Control Servers

Guaranteeing stability of control applications in embedded systems, or cyber-physical systems, is perhaps the alpha and omega of implementing such applications. However, as opposed to the classical real-time systems where often the acceptance criterion is meeting the deadline, control applications do not primarily enforce hard deadlines. In the case of control applications, stability is considered to be the main design criterion and can be expressed in terms of the amount of delay and jitter a control application can tolerate before instability. Therefore, new design and analysis techniques are required for embedded control systems. In this paper, the analysis and design of such systems considering server-based resource reservation mechanism are addressed. The benefits of employing servers are manifold: (1) providing a compositional framework, (2) protection against other tasks misbehaviors, and (3) systematic bandwidth assignment. We propose a methodology for designing bandwidth-efficient servers to stabilize control tasks

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