465 research outputs found
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 , where is the stellar radius and 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 is replaced by a 2-vector parametrizing the solutions.
We find that where . 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
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