Black hole tidal problem in the Fermi normal coordinates

We derive a tidal potential for a self-gravitating fluid star orbiting Kerr black hole along a timelike geodesic extending previous works by Fishbone and Marck. In this paper, the tidal potential is calculated up to the third and fourth-order terms in $R/r$, where $R$ is the stellar radius and $r$ the orbital separation, in the Fermi-normal coordinate system following the framework developed by Manasse and Misner. The new formulation is applied for determining the tidal disruption limit (Roche limit) of corotating Newtonian stars in circular orbits moving on the equatorial plane of Kerr black holes. It is demonstrated that the third and fourth-order terms quantitatively play an important role in the Roche limit for close orbits with R/r \agt 0.1. It is also indicated that the Roche limit of neutron stars orbiting a stellar-mass black hole near the innermost stable circular orbit may depend sensitively on the equation of state of the neutron star.Comment: Correct typo

Retarded coordinates based at a world line, and the motion of a small black hole in an external universe

In the first part of this article I present a system of retarded coordinates based at an arbitrary world line of an arbitrary curved spacetime. The retarded-time coordinate labels forward light cones that are centered on the world line, the radial coordinate is an affine parameter on the null generators of these light cones, and the angular coordinates are constant on each of these generators. The spacetime metric in the retarded coordinates is displayed as an expansion in powers of the radial coordinate and expressed in terms of the world line's acceleration vector and the spacetime's Riemann tensor evaluated at the world line. The formalism is illustrated in two examples, the first involving a comoving world line of a spatially-flat cosmology, the other featuring an observer in circular motion in the Schwarzschild spacetime. The main application of the formalism is presented in the second part of the article, in which I consider the motion of a small black hole in an empty external universe. I use the retarded coordinates to construct the metric of the small black hole perturbed by the tidal field of the external universe, and the metric of the external universe perturbed by the presence of the black hole. Matching these metrics produces the MiSaTaQuWa equations of motion for the small black hole.Comment: 20 pages, revtex4, 2 figure

Burst dynamics during drainage displacements in porous media: Simulations and experiments

We investigate the burst dynamics during drainage going from low to high injection rate at various fluid viscosities. The bursts are identified as pressure drops in the pressure signal across the system. We find that the statistical distribution of pressure drops scales according to other systems exhibiting self-organized criticality. The pressure signal was calculated by a network model that properly simulates drainage displacements. We compare our results with corresponding experiments.Comment: 7 pages, 4 figures. Submitted to Europhys. Let

Numerical models of irrotational binary neutron stars in general relativity

We report on general relativistic calculations of quasiequilibrium configurations of binary neutron stars in circular orbits with zero vorticity. These configurations are expected to represent realistic situations as opposed to corotating configurations. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The velocity field inside the stars is computed by solving an elliptical equation for the velocity scalar potential. Results are presented for sequences of constant baryon number (evolutionary sequences). Although the central density decreases much less with the binary separation than in the corotating case, it still decreases. Thus, no tendency is found for the stars to individually collapse to black hole prior to merger.Comment: Minor corrections, improved figure, 5 pages, REVTeX, Phys. Rev. Lett. in pres

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests

We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multi-domain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multi-domain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in details for a polytropic equation of state with gamma=2.Comment: Minor corrections, references updated, 42 pages, 25 PostScript figures, accepted for publication in Phys. Rev.

Transposition of the tendon of the M. tibialis posterior as an effective operative treatment of a drop foot

Objective. To evaluate the results of transposition of the tendon of the M. tibialis posterior in patients with a drop foot. Design. Descriptive, retrospective and follow-up investigation. Methods. Surgical treatment was carried out in 12 patients with a drop foot (9 women and 3 men, with an average age of 37 years) in the period 1986-1998. The aetiology of the drop foot was a traumatic or iatrogenic lesion of the peroneal nerve or sciatic nerve in 9 patients and in 3 patients spina bifida occulta, leprosy and a herniation of a lumbar disc respectively. None of the patients had important comorbidity. Treatment consisted of lengthening the Achilles tendon according to Huckstep, transposition of the tibial posterior tendon in two tails to the dorsomedial and dorsolateral side of the foot, and six weeks of immobilisation in plaster of Paris. Results. The postoperative period was without complications. The treatment improved the heel-toe steppage gait in all patients. None of the 10 patients who had used an orthosis preoperatively still used it at the time of the follow up. Fifty per cent of the patients acquired a dorsiflexion of the foot of more than 0°. The results were in accordance with those in the literature. Conclusion. Transposition of the tibial posterior tendon is a worthwhile alternative for those patients with a drop foot (and without important comorbidity) who cannot walk satisfactorily with an ankle-foot orthosis.</p

Transposition of the tendon of the M. tibialis posterior as an effective operative treatment of a drop foot

Objective. To evaluate the results of transposition of the tendon of the M. tibialis posterior in patients with a drop foot. Design. Descriptive, retrospective and follow-up investigation. Methods. Surgical treatment was carried out in 12 patients with a drop foot (9 women and 3 men, with an average age of 37 years) in the period 1986-1998. The aetiology of the drop foot was a traumatic or iatrogenic lesion of the peroneal nerve or sciatic nerve in 9 patients and in 3 patients spina bifida occulta, leprosy and a herniation of a lumbar disc respectively. None of the patients had important comorbidity. Treatment consisted of lengthening the Achilles tendon according to Huckstep, transposition of the tibial posterior tendon in two tails to the dorsomedial and dorsolateral side of the foot, and six weeks of immobilisation in plaster of Paris. Results. The postoperative period was without complications. The treatment improved the heel-toe steppage gait in all patients. None of the 10 patients who had used an orthosis preoperatively still used it at the time of the follow up. Fifty per cent of the patients acquired a dorsiflexion of the foot of more than 0°. The results were in accordance with those in the literature. Conclusion. Transposition of the tibial posterior tendon is a worthwhile alternative for those patients with a drop foot (and without important comorbidity) who cannot walk satisfactorily with an ankle-foot orthosis.</p