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

Quasiequilibrium sequences of black-hole--neutron-star binaries in general relativity

We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame. We present results for a binary with polytropic index n=1, mass ratio M_{irr}^{BH}/M_{B}^{NS}=5 and neutron star compaction M_{ADM,0}^{NS}/R_0=0.0879, where M_{irr}^{BH} is the irreducible mass of the black hole, M_{B}^{NS} the neutron star baryon rest-mass, and M_{ADM,0}^{NS} and R_0 the neutron star Arnowitt-Deser-Misner mass and areal radius in isolation, respectively. Our models represent valid solutions to Einstein's constraint equations and may therefore be employed as initial data for dynamical simulations of black hole-neutron star binaries.Comment: 5 pages, 1 figure, revtex4, published in Phys.Rev.

SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD BLACK HOLE

It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a non-rotating black hole is presented. The generalization to the case of the Kerr solution is presented too.Comment: 11 pages, 2 PostScript figures (available as uuencoded compressed tar file), uses epsfig.tex). Accepted on February 1995 for publication in Classical and Quantum Gravit

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

Quantification and prognostic relevance of angiogenic parameters in invasive cervical cancer.

Tumour stromal neovascularization was investigated in 114 invasive and 20 in situ carcinomas of the uterine cervix by staining representative sections with the specific endothelial marker anti CD31 (clone JC/70A, isotope IgG1). A digital image analyser was used to measure the immunoreactivity. The following parameters were determined in the 'hot spots': vessel counts, vessel perimeter and endothelial stained area (expressed per mm2). The results were correlated with clinical and histopathological data. There was no significant relationship between the histopathological findings (tumour histology, tumour differentiation, FIGO stage, presence of lymph node metastasis or lymphovascular space involvement) and the median vessel count. In a univariate analysis all angiogenesis parameters had prognostic value: a higher vascularity was associated with worse prognosis (P < 0.05). Multiple regression analysis showed that vascular permeation (P < 0.001) and the median vessel count (P = 0.005) were the most important prognostic indicators. In the future these criteria may be used for selection of patients for anti-angiogenesis therapy

Critical Percolation in High Dimensions

We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing which allowed us to simulate clusters of millions of sites on computers with less than 500 MB memory; (ii) a histogram method which allowed us to obtain information for several p values from a single simulation; and (iii) a new variance reduction technique which is especially efficient at high dimensions where it reduces error bars by a factor up to approximately 30 and more. Based on these data we propose a new scaling law for finite cluster size corrections.Comment: 5 pages including figures, RevTe

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

We present a semi-analytic study of the equilibrium models of close binary systems containing a fluid star (mass $m$ and radius $R_0$) and a Kerr black hole (mass $M$) in circular orbit. We consider the limit $M\gg m$ where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid, and satisfies the polytropic equation of state. The models also include fluid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron star-black hole binaries) to be constructed. Tidal disruption occurs at orbital radius $r_{\rm tide}\sim R_0(M/m)^{1/3}$, but the dimensionless ratio $\hat r_{\rm tide}=r_{\rm tide}/[R_0(M/m)^{1/3}]$ depends on the spin parameter of the black hole as well as on the equation of state and the internal rotation of the star. We find that the general relativistic tidal field disrupts the star at a larger $\hat r_{\rm tide}$ than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole's horizon. In general, $\hat r_{\rm tide}$ is smaller for a (prograde rotating) Kerr black hole than for a Schwarzschild black hole. We apply our results to coalescing black hole-neutron star and black hole-white dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma ray bursts which may result from such disruption.Comment: 29 pages including 8 figures. Minor changes and update. To appear in ApJ, March 20, 2000 (Vol.532, #1

An approximate binary-black-hole metric

An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric is presented in a single coordinate system valid up to the apparent horizons of the black holes. This metric could be useful in numerical simulations of binary black holes. Initial data extracted from this metric have the advantages of being linked to the early inspiral phase of the binary system, and of not containing spurious gravitational waves.Comment: 20 pages, 1 figure; some changes in Sec. IV B,C and Sec.