377 research outputs found
A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory
In the present paper we prove a classification (uniqueness) theorem for
stationary, asymptotically flat black hole spacetimes with connected and
non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary
dilaton coupling parameter . We show that such black holes are uniquely
specified by the length of the horizon interval, angular momentum, electric and
magnetic charge and the value of the dilaton field at infinity when the dilaton
coupling parameter satisfies . The proof is based on the
nonpositivity of the Riemann curvature operator on the space of the potentials.
A generalization of the classification theorem for spacetimes with disconnected
horizons is also given.Comment: 15 pages, v2 typos correcte
Differentially rotating disks of dust
We present a three-parameter family of solutions to the stationary
axisymmetric Einstein equations that describe differentially rotating disks of
dust. They have been constructed by generalizing the Neugebauer-Meinel solution
of the problem of a rigidly rotating disk of dust. The solutions correspond to
disks with angular velocities depending monotonically on the radial coordinate;
both decreasing and increasing behaviour is exhibited. In general, the
solutions are related mathematically to Jacobi's inversion problem and can be
expressed in terms of Riemann theta functions. A particularly interesting
two-parameter subfamily represents Baecklund transformations to appropriate
seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and
Gravitation". Second version with minor correction
Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes
We study two types of axially symmetric, stationary and asymptotically flat
spacetimes using highly accurate numerical methods. The one type contains a
black hole surrounded by a perfect fluid ring and the other a rigidly rotating
disc of dust surrounded by such a ring. Both types of spacetime are regular
everywhere (outside of the horizon in the case of the black hole) and fulfil
the requirements of the positive energy theorem. However, it is shown that both
the black hole and the disc can have negative Komar mass. Furthermore, there
exists a continuous transition from discs to black holes even when their Komar
masses are negative.Comment: 7 pages, 2 figures, document class iopart. v2: changes made
(including title) to coincide with published versio
Dirichlet Boundary Value Problems of the Ernst Equation
We demonstrate how the solution to an exterior Dirichlet boundary value
problem of the axisymmetric, stationary Einstein equations can be found in
terms of generalized solutions of the Backlund type. The proof that this
generalization procedure is valid is given, which also proves conjectures about
earlier representations of the gravitational field corresponding to rotating
disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in
equation (4
OBDD-Based Representation of Interval Graphs
A graph can be described by the characteristic function of the
edge set which maps a pair of binary encoded nodes to 1 iff the nodes
are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store
can lead to a (hopefully) compact representation. Given the OBDD as an
input, symbolic/implicit OBDD-based graph algorithms can solve optimization
problems by mainly using functional operations, e.g. quantification or binary
synthesis. While the OBDD representation size can not be small in general, it
can be provable small for special graph classes and then also lead to fast
algorithms. In this paper, we show that the OBDD size of unit interval graphs
is and the OBDD size of interval graphs is $O(\
| V \ | \log \ | V \ |)\Omega(\ | V \ | \log
\ | V \ |)O(\log \ | V \ |)O(\log^2 \ | V \ |)$ operations and
evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic
Concepts 201
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
The chromosphere: gateway to the corona, or the purgatory of solar physics?
I argue that one should attempt to understand the solar chromosphere not only
for its own sake, but also if one is interested in the physics of: the corona;
astrophysical dynamos; space weather; partially ionized plasmas; heliospheric
UV radiation; the transition region. I outline curious observations which I
personally find puzzling and deserving of attention.Comment: To appear in the proceedings of the 25th NSO Workshop "Chromospheric
Structure and Dynamics. From Old Wisdom to New Insights", Memorie della
Societa' Astronomica Italiana, Eds. Tritschler et a
Dynamics of charged fluids and 1/L perturbation expansions
Some features of the calculation of fluid dynamo systems in
magnetohydrodynamics are studied. In the coupled set of the ordinary linear
differential equations for the spherically symmetric dynamos, the
problem represented by the presence of the mixed (Robin) boundary conditions is
addressed and a new treatment for it is proposed. The perturbation formalism of
large expansions is shown applicable and its main technical steps are
outlined.Comment: 16 p
The Ernst equation and ergosurfaces
We show that analytic solutions \mcE of the Ernst equation with non-empty
zero-level-set of \Re \mcE lead to smooth ergosurfaces in space-time. In
fact, the space-time metric is smooth near a "Ernst ergosurface" if and
only if \mcE is smooth near and does not have zeros of infinite order
there.Comment: 23 pages, 4 figures; misprints correcte
Differentially rotating disks of dust: Arbitrary rotation law
In this paper, solutions to the Ernst equation are investigated that depend
on two real analytic functions defined on the interval [0,1]. These solutions
are introduced by a suitable limiting process of Backlund transformations
applied to seed solutions of the Weyl class. It turns out that this class of
solutions contains the general relativistic gravitational field of an arbitrary
differentially rotating disk of dust, for which a continuous transition to some
Newtonian disk exists. It will be shown how for given boundary conditions (i.
e. proper surface mass density or angular velocity of the disk) the
gravitational field can be approximated in terms of the above solutions.
Furthermore, particular examples will be discussed, including disks with a
realistic profile for the angular velocity and more exotic disks possessing two
spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and
Gravitation
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