On the black hole limit of rotating fluid bodies in equilibrium

Recently, it was shown that the extreme Kerr black hole is the only candidate for a (Kerr) black hole limit of stationary and axisymmetric, uniformly rotating perfect fluid bodies with a zero temperature equation of state. In this paper, necessary and sufficient conditions for reaching the black hole limit are presented.Comment: 8 pages, v2: one footnote and one reference added, accepted for publication in CQ

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

Ultraspinning instability of rotating black holes

Rapidly rotating Myers-Perry black holes in d>5 dimensions were conjectured to be unstable by Emparan and Myers. In a previous publication, we found numerically the onset of the axisymmetric ultraspinning instability in the singly-spinning Myers-Perry black hole in d=7,8,9. This threshold signals also a bifurcation to new branches of axisymmetric solutions with pinched horizons that are conjectured to connect to the black ring, black Saturn and other families in the phase diagram of stationary solutions. We firmly establish that this instability is also present in d=6 and in d=10,11. The boundary conditions of the perturbations are discussed in detail for the first time and we prove that they preserve the angular velocity and temperature of the original Myers-Perry black hole. This property is fundamental to establish a thermodynamic necessary condition for the existence of this instability in general rotating backgrounds. We also prove a previous claim that the ultraspinning modes cannot be pure gauge modes. Finally we find new ultraspinning Gregory-Laflamme instabilities of rotating black strings and branes that appear exactly at the critical rotation predicted by the aforementioned thermodynamic criterium. The latter is a refinement of the Gubser-Mitra conjecture.Comment: 38 pages, 6 figures, 1 tabl

The mass formula for quasi-black holes

A quasi-black hole, either non-extremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.Comment: 22 page

Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation

The first objective of this work is to obtain practical prescriptions to calculate the absorption of mass and angular momentum by a black hole when external processes produce gravitational radiation. These prescriptions are formulated in the time domain within the framework of black-hole perturbation theory. Two such prescriptions are presented. The first is based on the Teukolsky equation and it applies to general (rotating) black holes. The second is based on the Regge-Wheeler and Zerilli equations and it applies to nonrotating black holes. The second objective of this work is to apply the time-domain absorption formalisms to situations in which the black hole is either small or slowly moving. In the context of this small-hole/slow-motion approximation, the equations of black-hole perturbation theory can be solved analytically, and explicit expressions can be obtained for the absorption of mass and angular momentum. The changes in the black-hole parameters can then be understood in terms of an interaction between the tidal gravitational fields supplied by the external universe and the hole's tidally-induced mass and current quadrupole moments. For a nonrotating black hole the quadrupole moments are proportional to the rate of change of the tidal fields on the hole's world line. For a rotating black hole they are proportional to the tidal fields themselves.Comment: 36 pages, revtex4, no figures, final published versio

Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions

In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. In terms of the formalism of relativistic celestial mechanics developed by Damour, Soffel and Xu, and the framework established by Carter and Quintana the post Newtonian equations of the displacement field and the symmetric trace-free shear tensor are obtained. Corresponding post-Newtonian junction conditions at interfaces also the outer surface boundary conditions are presented. The PN junction condition is an extension of Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page

Rotating traversable wormholes

The general form of a stationary, axially symmetric traversable wormhole is discussed. This provides an explicit class of rotating wormholes that generalize the static, spherically symmetric ones first considered by Morris and Thorne. In agreement with general analyses, it is verified that such a wormhole generically violates the null energy condition at the throat. However, for suitable model wormholes, there can be classes of geodesics falling through it which do not encounter any energy-condition-violating matter. The possible presence of an ergoregion surrounding the throat is also noted.Comment: 15 pages, harvmac; 1 figure in PicTeX; minor changes; to appear in Phys. Rev.

A Toy Model for Blandford-Znajek Mechanism

A toy model for the Blandford-Znajek mechanism is investigated: a Kerr black hole with a toroidal electric current residing in a thin disk around the black hole. The toroidal electric current generates a poloidal magnetic field threading the black hole and disk. Due to the interaction of the magnetic field with remote charged particles, the rotation of the black hole and disk induces an electromotive force, which can power an astrophysical load at remote distance. The power of the black hole and disk is calculated. It is found that, for a wide range of parameters specifying the rotation of the black hole and the distribution of the electric current in the disk, the power of the disk exceeds the power of the black hole. The torque provided by the black hole and disk is also calculated. The torque of the disk is comparable to the torque of the black hole. As the disk loses its angular momentum, the mass of the disk gradually drifts towards the black hole and gets accreted. Ultimately the power comes from the gravitational binding energy between the disk and the black hole, as in the standard theory of accretion disk, instead of the rotational energy of the black hole. This suggests that the Blandford-Znajek mechanism may be less efficient in extracting energy from a rotating black hole with a thin disk. The limitations of our simple model and possible improvements deserved for future work are also discussed.Comment: 16 pages, 4 figures. Accepted for publication in Physical Review

An administrative data validation study of the accuracy of algorithms for identifying rheumatoid arthritis: the influence of the reference standard on algorithm performance

BACKGROUND: We have previously validated administrative data algorithms to identify patients with rheumatoid arthritis (RA) using rheumatology clinic records as the reference standard. Here we reassessed the accuracy of the algorithms using primary care records as the reference standard. METHODS: We performed a retrospective chart abstraction study using a random sample of 7500 adult patients under the care of 83 family physicians contributing to the Electronic Medical Record Administrative data Linked Database (EMRALD) in Ontario, Canada. Using physician-reported diagnoses as the reference standard, we computed and compared the sensitivity, specificity, and predictive values for over 100 administrative data algorithms for RA case ascertainment. RESULTS: We identified 69 patients with RA for a lifetime RA prevalence of 0.9%. All algorithms had excellent specificity (>97%). However, sensitivity varied (75-90%) among physician billing algorithms. Despite the low prevalence of RA, most algorithms had adequate positive predictive value (PPV; 51-83%). The algorithm of “[1 hospitalization RA diagnosis code] or [3 physician RA diagnosis codes with ≥1 by a specialist over 2 years]” had a sensitivity of 78% (95% CI 69–88), specificity of 100% (95% CI 100–100), PPV of 78% (95% CI 69–88) and NPV of 100% (95% CI 100–100). CONCLUSIONS: Administrative data algorithms for detecting RA patients achieved a high degree of accuracy amongst the general population. However, results varied slightly from our previous report, which can be attributed to differences in the reference standards with respect to disease prevalence, spectrum of disease, and type of comparator group

Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole

We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology and 2+1 black hole topology. Interestingly, we find that the different membrane-topologies are connected via phase transitions of the form first discussed by Choptuik in investigations of scalar field collapse. More precisely, we find a first order phase transition (finite mass gap) between wormhole topology and black hole topology; the intermediate membrane being an unstable wormhole collapsing to a black hole. Moreover, we find a second order phase transition (no mass gap) between Minkowski topology and black hole topology; the intermediate membrane being a naked singularity. For the membranes of black hole topology, we find a mass scaling relation analogous to that originally found by Choptuik. However, in our case the parameter $p$ is replaced by a 2-vector $\vec{p}$ parametrizing the solutions. We find that $Mass\propto|\vec{p}-\vec{p}_*|^\gamma$ where $\gamma\approx 0.66$. We also find a periodic wiggle in the scaling relation. Our results show that black hole formation as a critical phenomenon is far more general than expected.Comment: 15 pages, Latex, 4 figures include