On gravitomagnetic precession around black holes

We compute exactly the Lense-Thirring precession frequency for point masses in the Kerr metric, for arbitrary black hole mass and specific angular momentum. We show that this frequency, for point masses at or close to the innermost stable orbit, and for holes with moderate to extreme rotation, is less than, but comparable to the rotation frequency. Thus, if the quasi periodic oscillations (QPOs) observed in the modulation of the X-ray flux from some black holes candidates are due to Lense-Thirring precession of orbiting material, we predict that a separate, distinct QPO ought to be observed in each object.Comment: Accepted for publication in MNRAS. MN-Latex, 2 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

Limitations of Radar Coordinates

The construction of a radar coordinate system about the world line of an observer is discussed. Radar coordinates for a hyperbolic observer as well as a uniformly rotating observer are described in detail. The utility of the notion of radar distance and the admissibility of radar coordinates are investigated. Our results provide a critical assessment of the physical significance of radar coordinates.Comment: 12 pages, revtex and pictex macros, 3 pictex figures, 1 eps figure. Expanded versio

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

Self-forces from generalized Killing fields

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.Comment: 21 page

Emission vs Fermi coordinates: applications to relativistic positioning systems

A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi triad, as described by the Fermi metric. In the case of a Schwarzschild spacetime modeling the gravitational field around the Earth and an observer at rest at a fixed spacetime point, these coordinates realize a relativistic positioning system alternative to the current GPS system. The latter is indeed essentially conceived as Newtonian, so that it necessarily needs taking into account at least the most important relativistic effects through Post-Newtonian corrections to work properly. Previous results concerning emission coordinates in flat spacetime are thus extended to this more general situation. Furthermore, the mapping between spacetime coordinates and emission coordinates is completely determined by means of the world function, which in the case of a Fermi metric can be explicitly obtained.Comment: 12 pages iop style, 2 eps figures, to appear on Classical and Quantum Gravity, 200

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

A computational framework for two-dimensional random walks with restarts

The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. We propose an extension of the framework introduced in [D. A. Bini, S. Massei, and B. Meini, Math. Comp., 87 (2018), pp. 2811-2830] which allows us to deal with more general situations such as processes involving restart events. This is motivated by the need for modeling processes that can incur in unexpected failures like computer system reboots. We present a theoretical analysis of an enriched Banach algebra that, combined with appropriate algorithms, enables the numerical treatment of these problems. The results are applied to the solution of bidimensional quasi-birth-death processes with infinitely many phases which model random walks in the quarter plane, relying on the matrix analytic approach. The reliability of our approach is confirmed by extensive numerical experimentation on several case studies

Mechanics of extended masses in general relativity

The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress-energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain "effective metric" that is closely related to a non-perturbative generalization of the Detweiler-Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body's self-field is to finitely renormalize the "bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein's equation linearized about a vacuum background.Comment: 39 pages, 2 figures; fixed equation satisfied by the Green function used to construct the effective metri

Avaliação de impactos econômicos, sociais e ambientais de sistema de produção de morango orgânico em Pelotas, RS.

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